First, note that (almost) all my preprints are available on the archive.
Here is my list of publications in PDF format.
Next, you can find my PhD thesis, as well as my habilitation thesis.
Finally, you may prefer to browse my papers by theme:
Schubert calculus: (6 papers) | |
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Schubert puzzles and integrability III: separated descents \text{Schubert puzzles and integrability {III}: separated descents}(2023) @misc { artic83, arxiv = {2306.13855}, year = {2023}, title = {Schubert puzzles and integrability {III}: separated descents}, author = {Knutson, Allen and Zinn-Justin, Paul} } | |
Schubert puzzles and integrability II:
multiplying motivic Segre classes \text{Schubert puzzles and integrability {II}:
multiplying motivic {S}egre classes}(2021) @misc { artic80, arxiv = {2102.00563}, year = {2021}, title = {Schubert puzzles and integrability {II}: multiplying motivic {S}egre classes}, author = {Knutson, Allen and Zinn-Justin, Paul} } | |
Restricting Schubert classes to symplectic Grassmannians using self-dual puzzles \text{Restricting {S}chubert classes to symplectic {G}rassmannians using self-dual puzzles}in "Proceedings of the 5th Conference on Formal Power
Series and Algebraic Combinatorics (Ljubljana, 2019)" (2018) @inproceedings { artic73, url = {http://fpsac2019.fmf.uni-lj.si/resources/Proceedings/154.pdf}, booktitle = {Proceedings of the 5th {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({L}jubljana, 2019)}, year = {2018}, arxiv = {1811.07581}, title = {Restricting {S}chubert classes to symplectic {G}rassmannians using self-dual puzzles}, author = {Halacheva, Iva and Knutson, Allen and Zinn-Justin, Paul} } | |
Schubert puzzles and integrability I: invariant trilinear forms \text{Schubert puzzles and integrability {I}: invariant trilinear forms}(2017) @misc { artic71, year = {2017}, arxiv = {1706.10019}, title = {Schubert puzzles and integrability {I}: invariant trilinear forms}, author = {Knutson, Allen and Zinn-Justin, Paul} } | |
Littlewood–Richardson coefficients for Grothendieck polynomials from integrability \text{{L}ittlewood--{R}ichardson coefficients for {G}rothendieck polynomials from integrability}J. Reine Angew. Math. 757 (2019) 159–195@article { artic68, doi = {10.1515/crelle-2017-0033}, arxiv = {1607.02396}, pages = {159--195}, volume = {757}, fjournal = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, journal = {J. Reine Angew. Math.}, year = {2019}, title = {{L}ittlewood--{R}ichardson coefficients for {G}rothendieck polynomials from integrability}, author = {Wheeler, M. and Zinn-Justin, Paul} } | |
Littlewood–Richardson coefficients and integrable tilings \text{{L}ittlewood--{R}ichardson coefficients and integrable tilings}Electron. J. Combin. 16 (2009) Research Paper 12@article { artic46, pages = {Research Paper 12}, year = {2009}, volume = {16}, fjournal = {Electronic Journal of Combinatorics}, journal = {Electron. J. Combin.}, arxiv = {0809.2392}, title = {{L}ittlewood--{R}ichardson coefficients and integrable tilings}, author = {Zinn-Justin, Paul} } | |
Mathematical software: (1 papers) | |
The CotangentSchubert Macaulay2 package \text{The {C}otangent{S}chubert {M}acaulay2 package}(2021) @misc { artic82, url = {https://www.unimelb-macaulay2.cloud.edu.au/#tutorial-CotangentSchubert}, year = {2021}, title = {The {C}otangent{S}chubert {M}acaulay2 package}, author = {Zinn-Justin, Paul} } | |
Geometry and Quantum Integrable Systems: (12 papers) | |
Shuffle algebras, lattice paths and the commuting scheme \text{Shuffle algebras, lattice paths and the commuting scheme}(2021) @misc { artic81, arxiv = {2110.07155}, year = {2021}, title = {Shuffle algebras, lattice paths and the commuting scheme}, author = {Garbali, A. and Zinn-Justin, Paul} } | |
Higher spin sl_2 R-matrix from equivariant (co)homology \text{Higher spin {$\mathfrak{sl}_2$} {$R$}-matrix from equivariant (co)homology}Lett. Math. Phys. 110 (2020) 2435–2470@article { artic75, doi = {10.1007/s11005-020-01302-z}, pages = {2435--2470}, volume = {110}, fjournal = {Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics}, journal = {Lett. Math. Phys.}, year = {2020}, arxiv = {1904.11107}, title = {Higher spin {$\mathfrak{sl}_2$} {$R$}-matrix from equivariant (co)homology}, author = {Bykov, D. and Zinn-Justin, Paul} } | |
Loop models and K-theory \text{Loop models and {$K$}-theory}SIGMA Symmetry Integrability Geom. Methods Appl. 14 (2018) paper 69, 48@article { artic70, pages = {paper 69, 48}, volume = {14}, doi = {10.3842/SIGMA.2018.069}, fjournal = {SIGMA. Symmetry, Integrability and Geometry. Methods and Applications}, journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, arxiv = {1612.05361}, year = {2018}, title = {Loop models and {$K$}-theory}, author = {Zinn-Justin, Paul} } | |
Grassmann–Grassmann conormal varieties, integrability, and plane partitions \text{{G}rassmann--{G}rassmann conormal varieties, integrability, and plane partitions}Annales de l'Institut Fourier 69 (3) (2019) 1087-1145@article { artic69, language = {en}, zbl = {07067427}, doi = {10.5802/aif.3266}, pages = {1087-1145}, year = {2019}, number = {3}, volume = {69}, publisher = {Association des Annales de l'institut Fourier}, journal = {Annales de l'Institut Fourier}, arxiv = {1612.04465}, title = {{G}rassmann--{G}rassmann conormal varieties, integrability, and plane partitions}, author = {Knutson, Allen and Zinn-Justin, Paul} } | |
Quiver varieties and the quantum Knizhnik–Zamolodchikov equation \text{Quiver varieties and the quantum {K}nizhnik--{Z}amolodchikov equation}Theoretical and Mathematical Physics 185 (3) (2015) 1741–1758@article { artic64, pages = {1741--1758}, publisher = {Pleiades Publishing}, doi = {10.1007/s11232-015-0376-x}, number = {3}, volume = {185}, journal = {Theoretical and Mathematical Physics}, issn = {0040-5779}, year = {2015}, arxiv = {1502.01093}, title = {Quiver varieties and the quantum {K}nizhnik--{Z}amolodchikov equation}, author = {Zinn-Justin, Paul} } | |
Type C Brauer loop schemes and loop model with boundaries \text{Type {$\hat{\mathrm C}$} {B}rauer loop schemes and loop model with boundaries}Ann. Henri Poincare 3 (2) (2016) 163–255@article { artic62, fjournal = {Annales de l’Institut Henri Poincar\'e D}, pages = {163--255}, doi = {10.4171/AIHPD/28}, number = {2}, volume = {3}, year = {2016}, arxiv = {1410.0262}, journal = {Ann. Henri Poincar\'e}, title = {Type {$\hat{\mathrm C}$} {B}rauer loop schemes and loop model with boundaries}, author = {Ponsaing, A. and Zinn-Justin, Paul} } | |
Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral \text{Extended {J}oseph polynomials, quantized conformal blocks, and a {$q$}-{S}elberg type integral}J. Geom. Phys. 62 (11) (2012) 2188–2207@article { artic56, doi = {10.1016/j.geomphys.2012.06.008}, arxiv = {1110.2187}, mrnumber = {2964653}, mrclass = {81T40 (17B81)}, coden = {JGPHE5}, issn = {0393-0440}, pages = {2188--2207}, number = {11}, year = {2012}, volume = {62}, fjournal = {Journal of Geometry and Physics}, journal = {J. Geom. Phys.}, title = {Extended {J}oseph polynomials, quantized conformal blocks, and a {$q$}-{S}elberg type integral}, author = {Rim{\'a}nyi, R. and Tarasov, V. and Varchenko, A. and Zinn-Justin, Paul} } | |
The Brauer loop scheme and orbital varieties \text{The {B}rauer loop scheme and orbital varieties}J. Geom. Phys. 78 (2014) 80–110@article { artic39, doi = {10.1016/j.geomphys.2014.01.006}, arxiv = {1001.3335}, pages = {80--110}, volume = {78}, fjournal = {Journal of Geometry and Physics}, journal = {J. Geom. Phys.}, year = {2014}, title = {The {B}rauer loop scheme and orbital varieties}, author = {Knutson, Allen and Zinn-Justin, Paul} } | |
From Orbital Varieties to Alternating Sign Matrices \text{From Orbital Varieties to Alternating Sign Matrices}in "Proceedings of the 5th Conference on Formal Power
Series and Algebraic Combinatorics (San Diego, 2006)" (2006) @inproceedings { artic35, year = {2006}, url = {http://www-igm.univ-mlv.fr/~fpsac/FPSAC06/SITE06/papers/60.pdf}, arxiv = {math-ph/0512047}, booktitle = {Proceedings of the 5th {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({S}an {D}iego, 2006)}, title = {From Orbital Varieties to Alternating Sign Matrices}, author = {Di Francesco, P. and Zinn-Justin, Paul} } | |
Quantum Knizhnik–Zamolodchikov equation, generalized
Razumov–Stroganov sum rules and extended Joseph
polynomials \text{Quantum {K}nizhnik--{Z}amolodchikov equation, generalized
{R}azumov--{S}troganov sum rules and extended {J}oseph
polynomials}J. Phys. A 38 (48) (2005) L815–L822@article { artic34, doi = {10.1088/0305-4470/38/48/L02}, arxiv = {math-ph/0508059}, mrreviewer = {G. K. Giorgadze}, mrnumber = {MR2185933 (2006m:82019)}, mrclass = {82B20 (05A19 81R12 81R50)}, coden = {JPHAC5}, issn = {0305-4470}, pages = {L815--L822}, number = {48}, year = {2005}, volume = {38}, fjournal = {Journal of Physics. A. Mathematical and General}, journal = {J. Phys. A}, title = {Quantum {K}nizhnik--{Z}amolodchikov equation, generalized {R}azumov--{S}troganov sum rules and extended {J}oseph polynomials}, author = {Di Francesco, P. and Zinn-Justin, Paul} } | |
A scheme related to the Brauer loop model \text{A scheme related to the {B}rauer loop model}Adv. Math. 214 (1) (2007) 40–77@article { artic33, arxiv = {math.AG/0503224}, mrreviewer = {Dmitri I. Panyushev}, mrnumber = {MR2348022 (2008j:14097)}, mrclass = {14M99 (14C17 82B20 82B23)}, coden = {ADMTA4}, issn = {0001-8708}, pages = {40--77}, number = {1}, year = {2007}, volume = {214}, fjournal = {Advances in Mathematics}, journal = {Adv. Math.}, title = {A scheme related to the {B}rauer loop model}, author = {Knutson, Allen and Zinn-Justin, Paul} } | |
Inhomogeneous model of crossing loops and multidegrees of some
algebraic varieties \text{Inhomogeneous model of crossing loops and multidegrees of some
algebraic varieties}Comm. Math. Phys. 262 (2) (2006) 459–487@article { artic32, arxiv = {math-ph/0412031}, mrreviewer = {Sergei K. Lando}, mrnumber = {MR2200268 (2006k:82068)}, mrclass = {82B41}, coden = {CMPHAY}, issn = {0010-3616}, pages = {459--487}, number = {2}, year = {2006}, volume = {262}, fjournal = {Communications in Mathematical Physics}, journal = {Comm. Math. Phys.}, title = {Inhomogeneous model of crossing loops and multidegrees of some algebraic varieties}, author = {Di Francesco, P. and Zinn-Justin, Paul} } | |
Symmetric functions and Quantum Integrable Systems: (5 papers) | |
Vertex models for Canonical Grothendieck polynomials and their duals \text{Vertex models for Canonical {G}rothendieck polynomials and their duals}(2020) @misc { artic79, arxiv = {2009.13172}, year = {2020}, title = {Vertex models for Canonical {G}rothendieck polynomials and their duals}, author = {Gunna, A. and Zinn-Justin, Paul} } | |
Honeycombs for Hall polynomials \text{Honeycombs for {H}all polynomials}Electron. J. Combin. 27 (2019) P2.23@article { artic76, doi = {10.37236/9040}, pages = {P2.23}, year = {2019}, volume = {27}, fjournal = {Electronic Journal of Combinatorics}, journal = {Electron. J. Combin.}, arxiv = {1909.10720}, title = {Honeycombs for {H}all polynomials}, author = {Zinn-Justin, Paul} } | |
Hall polynomials, inverse Kostka polynomials and puzzles \text{{H}all polynomials, inverse {K}ostka polynomials and puzzles}Journal of Combinatorial Theory, Series A 159 (2018) 107–163@article { artic67, arxiv = {1603.01815}, doi = {https://doi.org/10.1016/j.jcta.2018.05.005}, issn = {0097-3165}, year = {2018}, pages = {107--163}, volume = {159}, journal = {Journal of Combinatorial Theory, Series A}, title = {{H}all polynomials, inverse {K}ostka polynomials and puzzles}, author = {Wheeler, M. and Zinn-Justin, Paul} } | |
Refined Cauchy/Littlewood identities and six-vertex model partition
functions: III. Deformed bosons \text{Refined {C}auchy/{L}ittlewood identities and six-vertex model partition
functions: {III}. Deformed bosons}Adv. Math. 299 (2016) 543–600@article { artic65, abstract = {We study Hall–Littlewood polynomials using an integrable lattice model of t-deformed bosons. Working with row-to-row transfer matrices, we review the construction of Hall–Littlewood polynomials (of the A n root system) within the framework of this model. Introducing appropriate double-row transfer matrices, we extend this formalism to Hall–Littlewood polynomials based on the B C n root system, and obtain a new combinatorial formula for them. We then apply our methods to prove a series of refined Cauchy and Littlewood identities involving Hall–Littlewood polynomials. The last two of these identities are new, and relate infinite sums over hyperoctahedrally symmetric Hall–Littlewood polynomials with partition functions of the six-vertex model on finite domains.}, keywords = {Cauchy and Littlewood identities}, doi = {10.1016/j.aim.2016.05.010}, issn = {0001-8708}, pages = {543--600}, volume = {299}, fjournal = {Advances in Mathematics}, journal = {Adv. Math.}, year = {2016}, arxiv = {1508.02236}, title = {Refined {C}auchy/{L}ittlewood identities and six-vertex model partition functions: {III}. Deformed bosons}, author = {Wheeler, M. and Zinn-Justin, Paul} } | |
Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures \text{Refined {C}auchy/{L}ittlewood identities and six-vertex model partition functions: {II}. Proofs and new conjectures}Journal of Algebraic Combinatorics (2015) 1–49@article { artic61, pages = {1--49}, journal = {Journal of Algebraic Combinatorics}, issn = {0925-9899}, doi = {10.1007/s10801-015-0592-3}, year = {2015}, arxiv = {1405.7035}, title = {Refined {C}auchy/{L}ittlewood identities and six-vertex model partition functions: {II}. Proofs and new conjectures}, author = {Betea, D. and Wheeler, M. and Zinn-Justin, Paul} } | |
Statistical Models on Random Lattices: (7 papers) | |
The six-vertex model on random planar maps revisited \text{The six-vertex model on random planar maps revisited}(2020) @misc { artic78, arxiv = {2007.07928}, year = {2020}, title = {The six-vertex model on random planar maps revisited}, author = {Elvey Price, A. and Zinn-Justin, Paul} } | |
Eulerian orientations and the six-vertex model on planar maps \text{Eulerian orientations and the six-vertex model on planar maps}in "Proceedings of the 5th Conference on Formal Power
Series and Algebraic Combinatorics (Ljubljana, 2019)" (2019) @inproceedings { artic74, url = {http://fpsac2019.fmf.uni-lj.si/resources/Proceedings/129.pdf}, arxiv = {1902.07369}, year = {2019}, booktitle = {Proceedings of the 5th {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({L}jubljana, 2019)}, title = {Eulerian orientations and the six-vertex model on planar maps}, author = {Bousquet-M\'elou, M. and Elvey Price, A. and Zinn-Justin, Paul} } | |
Loop models, random matrices and planar algebras \text{Loop models, random matrices and planar algebras}Comm. Math. Phys. 316 (1) (2012) 45–97@article { artic54, year = {2012}, arxiv = {1012.0619}, doi = {10.1007/s00220-012-1573-1}, mrnumber = {2989453}, mrclass = {82Bxx (46Lxx 60B20)}, coden = {CMPHAY}, issn = {0010-3616}, pages = {45--97}, number = {1}, volume = {316}, fjournal = {Communications in Mathematical Physics}, journal = {Comm. Math. Phys.}, title = {Loop models, random matrices and planar algebras}, author = {Guionnet, A. and Jones, V. and Shlyakhtenko, D. and Zinn-Justin, Paul} } | |
The asymmetric ABAB matrix model \text{The asymmetric {$ABAB$} matrix model}Europhys. Lett. 64 (6) (2003) 737–742@article { artic26, arxiv = {hep-th/0308132}, mrnumber = {MR2030895 (2005a:82043)}, mrclass = {82B41 (83C80)}, issn = {0295-5075}, pages = {737--742}, number = {6}, year = {2003}, volume = {64}, fjournal = {Europhysics Letters}, journal = {Europhys. Lett.}, title = {The asymmetric {$ABAB$} matrix model}, author = {Zinn-Justin, Paul} } | |
The six-vertex model on random lattices \text{The six-vertex model on random lattices}Europhys. Lett. 50 (1) (2000) 15–21@article { artic10, arxiv = {cond-mat/9909250}, mrnumber = {MR1747830 (2001a:82046)}, mrclass = {82B44 (81T40 82B20)}, issn = {0295-5075}, pages = {15--21}, number = {1}, year = {2000}, volume = {50}, fjournal = {Europhysics Letters}, journal = {Europhys. Lett.}, title = {The six-vertex model on random lattices}, author = {Zinn-Justin, Paul} } | |
The dilute Potts model on random surfaces \text{The dilute {P}otts model on random surfaces}J. Statist. Phys. 98 (1-2) (2000) j10–264@article { artic07, arxiv = {cond-mat/9903385}, mrnumber = {MR1745840 (2002a:82067)}, mrclass = {82B44 (82B20)}, coden = {JSTPSB}, issn = {0022-4715}, pages = {j10--264}, number = {1-2}, year = {2000}, volume = {98}, fjournal = {Journal of Statistical Physics}, journal = {J. Statist. Phys.}, title = {The dilute {P}otts model on random surfaces}, author = {Zinn-Justin, Paul} } | |
Two-matrix model with ABAB interaction \text{Two-matrix model with {$ABAB$} interaction}Nuclear Phys. B 546 (3) (1999) 647–668@article { artic05, arxiv = {hep-th/9808043}, mrnumber = {MR1690386 (2000i:81083)}, mrclass = {81T10 (81T40)}, coden = {NUPBBO}, issn = {0550-3213}, pages = {647--668}, number = {3}, year = {1999}, volume = {546}, fjournal = {Nuclear Physics. B}, journal = {Nuclear Phys. B}, title = {Two-matrix model with {$ABAB$} interaction}, author = {Kazakov, V. and Zinn-Justin, Paul} } | |
Quantum Integrable Systems: (8 papers) | |
The trigonometric E_8 R-matrix \text{The trigonometric {$E_8$} {$R$}-matrix}Lett. Math. Phys. 110 (2020) 3279–3305@article { artic77, doi = {10.1007/s11005-020-01330-9}, pages = {3279--3305}, volume = {110}, fjournal = {Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics}, journal = {Lett. Math. Phys.}, arxiv = {2004.02044}, year = {2020}, title = {The trigonometric {$E_8$} {$R$}-matrix}, author = {Zinn-Justin, Paul} } | |
Theta function solutions of the quantum Knizhnik–Zamolodchikov–Bernard equation for a face model \text{Theta function solutions of the quantum {K}nizhnik--{Z}amolodchikov--{B}ernard equation for a face model}J. Phys. A 49 (6) (2016) @article { artic66, doi = {10.1088/1751-8113/49/6/064001}, number = {6}, volume = {49}, fjournal = {Journal of Physics. A. Mathematical and Theoretical}, journal = {J. Phys. A}, arxiv = {1509.04594}, year = {2016}, title = {Theta function solutions of the quantum {K}nizhnik--{Z}amolodchikov--{B}ernard equation for a face model}, author = {Finch, P. and Weston, R. and Zinn-Justin, Paul} } | |
Discrete holomorphicity and quantized affine algebras \text{Discrete holomorphicity and quantized affine algebras}J. Phys. A 46 (26) (2013) 265205@article { artic60, doi = {10.1088/1751-8113/46/26/265205}, number = {26}, volume = {46}, fjournal = {Journal of Physics. A. Mathematical and Theoretical}, journal = {J. Phys. A}, pages = {265205}, year = {2013}, arxiv = {1302.4649}, title = {Discrete holomorphicity and quantized affine algebras}, author = {Ikhlef, Y. and Weston, R. and Wheeler, M. and Zinn-Justin, Paul} } | |
Higher spin polynomial solutions of quantum Knizhnik–Zamolodchikov
equation \text{Higher spin polynomial solutions of quantum {K}nizhnik--{Z}amolodchikov
equation}Comm. Math. Phys. 328 (3) (2014) 1079–1115@article { artic59, doi = {10.1007/s00220-014-1963-7}, year = {2014}, pages = {1079--1115}, number = {3}, volume = {328}, fjournal = {Communications in Mathematical Physics}, journal = {Comm. Math. Phys.}, arxiv = {1212.4672}, title = {Higher spin polynomial solutions of quantum {K}nizhnik--{Z}amolodchikov equation}, author = {Fonseca, T. and Zinn-Justin, Paul} } | |
On some ground state components of the O(1) loop model \text{On some ground state components of the {$O(1)$} loop model}J. Stat. Mech. Theory Exp. (2009) P03025@article { artic47, pages = {P03025}, fjournal = {Journal of Statistical Mechanics: Theory and Experiment}, journal = {J. Stat. Mech. Theory Exp.}, year = {2009}, arxiv = {0901.1679}, title = {On some ground state components of the {$O(1)$} loop model}, author = {Fonseca, T. and Zinn-Justin, Paul} } | |
Polynomial solutions of qKZ equation and ground state of
XXZ spin chain at =-1/2 \text{Polynomial solutions of {$q$KZ} equation and ground state of
{$XXZ$} spin chain at {$\Delta=-1/2$}}J. Phys. A 40 (39) (2007) 11827–11847@article { artic42, doi = {10.1088/1751-8113/40/39/009}, arxiv = {0704.3542}, mrnumber = {MR2374053}, mrclass = {81R12 (17B81 81R10 82B20 82B23)}, issn = {1751-8113}, pages = {11827--11847}, number = {39}, year = {2007}, volume = {40}, fjournal = {Journal of Physics. A. Mathematical and Theoretical}, journal = {J. Phys. A}, title = {Polynomial solutions of {$q$KZ} equation and ground state of {$XXZ$} spin chain at {$\Delta=-1/2$}}, author = {Razumov, A. and Stroganov, Yu. and Zinn-Justin, Paul} } | |
Nonlinear integral equations for complex affine Toda models
associated with simply laced Lie algebras \text{Nonlinear integral equations for complex affine {T}oda models
associated with simply laced {L}ie algebras}J. Phys. A 31 (31) (1998) 6747–6770@article { artic04, arxiv = {hep-th/9712222}, mrreviewer = {Andrey V. Tsiganov}, mrnumber = {MR1643832 (99k:82017)}, mrclass = {82B20 (17B81 81R50 82B23)}, coden = {JPHAC5}, issn = {0305-4470}, pages = {6747--6770}, number = {31}, year = {1998}, volume = {31}, fjournal = {Journal of Physics. A. Mathematical and General}, journal = {J. Phys. A}, title = {Nonlinear integral equations for complex affine {T}oda models associated with simply laced {L}ie algebras}, author = {Zinn-Justin, Paul} } | |
The generalized multi-channel Kondo model: thermodynamics
and fusion equations \text{The generalized multi-channel {K}ondo model: thermodynamics
and fusion equations}Nuclear Phys. B 528 (3) (1998) 648–682@article { artic03, arxiv = {cond-mat/9801158}, mrnumber = {MR1643667 (2000i:82085)}, mrclass = {82D35 (81R50 82B10)}, coden = {NUPBBO}, issn = {0550-3213}, pages = {648--682}, number = {3}, year = {1998}, volume = {528}, fjournal = {Nuclear Physics. B}, journal = {Nuclear Phys. B}, title = {The generalized multi-channel {K}ondo model: thermodynamics and fusion equations}, author = {Zinn-Justin, Paul and Andrei, N.} } | |
Pattern-avoiding permutations: (1 papers) | |
1324-avoiding permutations revisited \text{1324-avoiding permutations revisited}Advances in Applied Mathematics 96 (2018) 312–333@article { artic72, doi = {10.1016/j.aam.2018.01.002}, issn = {0196-8858}, year = {2018}, pages = {312--333}, volume = {96}, journal = {Advances in Applied Mathematics}, arxiv = {1709.01248}, title = {1324-avoiding permutations revisited}, author = {Conway, A. and Guttmann, A. and Zinn-Justin, Paul} } | |
Random Matrix Theory: (4 papers) | |
Equilibrium problems for Raney densities \text{Equilibrium problems for {R}aney densities}Nonlinearity 28 (7) (2015) 2265@article { artic63, year = {2015}, doi = {10.1088/0951-7715/28/7/2265}, pages = {2265}, number = {7}, volume = {28}, journal = {Nonlinearity}, arxiv = {1411.4091}, title = {Equilibrium problems for {R}aney densities}, author = {Forrester, P. and Dang-Zheng, L. and Zinn-Justin, Paul} } | |
Adding and multiplying random matrices: a generalization of
Voiculescu's formulas \text{Adding and multiplying random matrices: a generalization of
{V}oiculescu's formulas}Phys. Rev. E (3) 59 (5, part A) (1999) 4884–4888@article { artic06, arxiv = {math-ph/9810010}, mrnumber = {MR1682207 (2000h:82043)}, mrclass = {82B41 (46L53 46L60)}, coden = {PLEEE8}, issn = {1539-3755}, pages = {4884--4888}, number = {5, part A}, year = {1999}, volume = {59}, fjournal = {Physical Review E. Statistical, Nonlinear, and Soft Matter Physics}, journal = {Phys. Rev. E (3)}, title = {Adding and multiplying random matrices: a generalization of {V}oiculescu's formulas}, author = {Zinn-Justin, Paul} } | |
Universality of correlation functions of Hermitian random
matrices in an external field \text{Universality of correlation functions of {H}ermitian random
matrices in an external field}Comm. Math. Phys. 194 (3) (1998) 631–650@article { artic02, arxiv = {cond-mat/9705044}, mrreviewer = {Aernout C. D. van Enter}, mrnumber = {MR1631489 (2000e:82029a)}, mrclass = {82B44 (60H25 82D30)}, coden = {CMPHAY}, issn = {0010-3616}, pages = {631--650}, number = {3}, year = {1998}, volume = {194}, fjournal = {Communications in Mathematical Physics}, journal = {Comm. Math. Phys.}, title = {Universality of correlation functions of {H}ermitian random matrices in an external field}, author = {Zinn-Justin, Paul} } | |
Random Hermitian matrices in an external field \text{Random {H}ermitian matrices in an external field}Nuclear Phys. B 497 (3) (1997) 725–732@article { artic01, arxiv = {cond-mat/9703033}, mrreviewer = {Aernout C. D. van Enter}, mrnumber = {MR1463645 (98k:82100)}, mrclass = {82B44 (82B41)}, coden = {NUPBBO}, issn = {0550-3213}, pages = {725--732}, number = {3}, year = {1997}, volume = {497}, fjournal = {Nuclear Physics. B}, journal = {Nuclear Phys. B}, title = {Random {H}ermitian matrices in an external field}, author = {Zinn-Justin, Paul} } | |
Combinatorics and Quantum Integrable Systems: (12 papers) | |
A doubly refined enumeration of Alternating Sign Matrices and Descending Plane Partitions \text{A doubly refined enumeration of Alternating Sign Matrices and Descending Plane Partitions}J. Combin. Theory Ser. A 120 (2) (2013) 409–432@article { artic58, fjournal = {Journal of Combinatorial Theory. Series A}, journal = {J. Combin. Theory Ser. A}, mrnumber = {2995049}, doi = {10.1016/j.jcta.2012.09.004}, year = {2013}, coden = {JCBTA7}, issn = {0097-3165}, pages = {409--432}, number = {2}, volume = {120}, arxiv = {1202.1520}, title = {A doubly refined enumeration of Alternating Sign Matrices and Descending Plane Partitions}, author = {Behrend, R. and Di Francesco, P. and Zinn-Justin, Paul} } | |
Sum rule for the eight-vertex model on its combinatorial line \text{Sum rule for the eight-vertex model on its combinatorial line}Springer Proceedings in Mathematics and Statistics in "Symmetries, Integrable systems and representations" 40 (2013) @inproceedings { artic57, volume = {40}, year = {2013}, note = {Eds Iohara, Morier-Genoud, R{\'e}my}, arxiv = {1202.4420}, journal = {Springer Proceedings in Mathematics and Statistics}, booktitle = {Symmetries, Integrable systems and representations}, title = {Sum rule for the eight-vertex model on its combinatorial line}, author = {Zinn-Justin, Paul} } | |
On the weighted enumeration of Alternating Sign Matrices and Descending Plane Partitions \text{On the weighted enumeration of Alternating Sign Matrices and Descending Plane Partitions}J. Combin. Theory Ser. A 119 (2) (2012) 331–363@article { artic55, arxiv = {1103.1176}, mrnumber = {2860598}, mrclass = {05A15 (05A17 05B20)}, coden = {JCBTA7}, doi = {10.1016/j.jcta.2011.09.004}, issn = {0097-3165}, year = {2012}, pages = {331--363}, number = {2}, volume = {119}, fjournal = {Journal of Combinatorial Theory. Series A}, journal = {J. Combin. Theory Ser. A}, title = {On the weighted enumeration of Alternating Sign Matrices and Descending Plane Partitions}, author = {Behrend, R. and Di Francesco, P. and Zinn-Justin, Paul} } | |
On the Doubly Refined Enumeration of Alternating Sign Matrices and
Totally Symmetric Self-Complementary Plane Partitions \text{On the Doubly Refined Enumeration of {A}lternating {S}ign {M}atrices and
{T}otally {S}ymmetric {S}elf-{C}omplementary {P}lane {P}artitions}Electron. J. Combin. 15 (2008) Research Paper 81, 35 pp@article { artic45, mrnumber = {MR2411458}, mrclass = {05A15 (15A51 82B20)}, issn = {1077-8926}, pages = {Research Paper 81, 35 pp}, year = {2008}, volume = {15}, fjournal = {Electronic Journal of Combinatorics}, journal = {Electron. J. Combin.}, arxiv = {0803.1595}, title = {On the Doubly Refined Enumeration of {A}lternating {S}ign {M}atrices and {T}otally {S}ymmetric {S}elf-{C}omplementary {P}lane {P}artitions}, author = {Fonseca, T. and Zinn-Justin, Paul} } | |
Punctured plane partitions and the q-deformed Knizhnik–Zamolodchikov and Hirota equations \text{Punctured plane partitions and the {$q$}-deformed {K}nizhnik--{Z}amolodchikov and {H}irota equations}J. Combin. Theory Ser. A 116 (4) (2009) 772–794@article { artic44, arxiv = {0712.3584}, doi = {10.1016/j.jcta.2008.11.008}, mrnumber = {2513634 (2010k:05028)}, mrclass = {05A17 (33D80 39A13)}, coden = {JCBTA7}, issn = {0097-3165}, pages = {772--794}, number = {4}, year = {2009}, volume = {116}, fjournal = {Journal of Combinatorial Theory. Series A}, journal = {J. Combin. Theory Ser. A}, title = {Punctured plane partitions and the {$q$}-deformed {K}nizhnik--{Z}amolodchikov and {H}irota equations}, author = {de Gier, J. and Pyatov, P. and Zinn-Justin, Paul} } | |
Quantum Knizhnik–Zamolodchikov equation: reflecting
boundary conditions and combinatorics \text{Quantum {K}nizhnik--{Z}amolodchikov equation: reflecting
boundary conditions and combinatorics}J. Stat. Mech. Theory Exp. (12) (2007) P12009, 30 pp@article { artic43, doi = {10.1088/1742-5468/2007/12/P12009}, arxiv = {0709.3410}, mrnumber = {MR2367185}, mrclass = {81R12 (82B20 82B23 82D60)}, issn = {1742-5468}, pages = {P12009, 30 pp}, number = {12}, year = {2007}, fjournal = {Journal of Statistical Mechanics: Theory and Experiment}, journal = {J. Stat. Mech. Theory Exp.}, title = {Quantum {K}nizhnik--{Z}amolodchikov equation: reflecting boundary conditions and combinatorics}, author = {Di Francesco, P. and Zinn-Justin, Paul} } | |
Quantum Knizhnik–Zamolodchikov equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices \text{Quantum {K}nizhnik--{Z}amolodchikov equation, {T}otally {S}ymmetric {S}elf-{C}omplementary {P}lane {P}artitions and {A}lternating {S}ign {M}atrices}Theor. Math. Phys. 154 (3) (2008) 331–348@article { artic41, doi = {10.1007/s11232-008-0031-x}, number = {3}, volume = {154}, pages = {331--348}, year = {2008}, fjournal = {Theoretical and Mathematical Physics}, journal = {Theor. Math. Phys.}, arxiv = {math-ph/0703015}, title = {Quantum {K}nizhnik--{Z}amolodchikov equation, {T}otally {S}ymmetric {S}elf-{C}omplementary {P}lane {P}artitions and {A}lternating {S}ign {M}atrices}, author = {Di Francesco, P. and Zinn-Justin, Paul} } | |
Loop model with mixed boundary conditions, qKZ
equation and alternating sign matrices \text{Loop model with mixed boundary conditions, {$q$KZ}
equation and alternating sign matrices}J. Stat. Mech. Theory Exp. (1) (2007) P01007, 16 pp@article { artic40, doi = {10.1088/1742-5468/2007/01/P01007}, arxiv = {math-ph/0610067}, mrreviewer = {Alexei P. Isaev}, mrnumber = {MR2284004}, mrclass = {82B23 (05A15 82B20)}, issn = {1742-5468}, pages = {P01007, 16 pp}, number = {1}, year = {2007}, fjournal = {Journal of Statistical Mechanics: Theory and Experiment}, journal = {J. Stat. Mech. Theory Exp.}, title = {Loop model with mixed boundary conditions, {$q$KZ} equation and alternating sign matrices}, author = {Zinn-Justin, Paul} } | |
Proof of the Razumov–Stroganov conjecture for some
infinite families of link patterns \text{Proof of the {R}azumov--{S}troganov conjecture for some
infinite families of link patterns}Electron. J. Combin. 13 (1) (2006) Research Paper 110, 15 pp@article { artic38, arxiv = {math/0607183}, mrreviewer = {Azer Kerimov}, mrnumber = {MR2274325 (2007k:82034)}, mrclass = {82B23 (05A19 52C20)}, issn = {1077-8926}, pages = {Research Paper 110, 15 pp}, number = {1}, year = {2006}, volume = {13}, fjournal = {Electronic Journal of Combinatorics}, journal = {Electron. J. Combin.}, title = {Proof of the {R}azumov--{S}troganov conjecture for some infinite families of link patterns}, author = {Zinn-Justin, Paul} } | |
Combinatorial point for fused loop models \text{Combinatorial point for fused loop models}Comm. Math. Phys. 272 (3) (2007) 661–682@article { artic37, doi = {10.1007/s00220-007-0225-3}, arxiv = {math-ph/0603018}, mrnumber = {MR2304471}, mrclass = {05Exx (17Bxx 82B20 82B23)}, coden = {CMPHAY}, issn = {0010-3616}, pages = {661--682}, number = {3}, year = {2007}, volume = {272}, fjournal = {Communications in Mathematical Physics}, journal = {Comm. Math. Phys.}, title = {Combinatorial point for fused loop models}, author = {Zinn-Justin, Paul} } | |
Sum Rules for the Ground States of the O(1) Loop Model on a Cylinder and the XXZ Spin Chain \text{Sum Rules for the Ground States of the {$O(1)$} Loop Model on a Cylinder and the {XXZ} Spin Chain}J. Stat. Mech. (2006) P08011@article { artic36, doi = {10.1088/1742-5468/2006/08/P08011}, year = {2006}, arxiv = {math-ph/0603009}, pages = {P08011}, journal = {J. Stat. Mech.}, title = {Sum Rules for the Ground States of the {$O(1)$} Loop Model on a Cylinder and the {XXZ} Spin Chain}, author = {Francesco, P. Di and Zinn-Justin, P. and Zuber, J.-B.} } | |
Around the Razumov–Stroganov conjecture: proof of a
multi-parameter sum rule \text{Around the {R}azumov--{S}troganov conjecture: proof of a
multi-parameter sum rule}Electron. J. Combin. 12 (2005) Research Paper 6, 27 pp@article { artic31, url = {http://www.combinatorics.org/Volume_12/Abstracts/v12i1r6.html}, arxiv = {math-ph/0410061}, mrreviewer = {Sergei K. Lando}, mrnumber = {MR2134169 (2005m:82017)}, mrclass = {82B20 (05A19 52C20)}, issn = {1077-8926}, pages = {Research Paper 6, 27 pp}, year = {2005}, volume = {12}, fjournal = {Electronic Journal of Combinatorics}, journal = {Electron. J. Combin.}, title = {Around the {R}azumov--{S}troganov conjecture: proof of a multi-parameter sum rule}, author = {Di Francesco, P. and Zinn-Justin, Paul} } | |
Six-Vertex model: (5 papers) | |
The arctic curve of the domain-wall six-vertex model in its
anti-ferroelectric regime \text{The arctic curve of the domain-wall six-vertex model in its
anti-ferroelectric regime}J. Stat. Mech. Theory Exp. (2010) L03002@article { artic53, pages = {L03002}, fjournal = {Journal of Statistical Mechanics: Theory and Experiment}, journal = {J. Stat. Mech. Theory Exp.}, arxiv = {1001.2189}, year = {2010}, title = {The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime}, author = {Colomo, F. and Pronko, G. and Zinn-Justin, Paul} } | |
The Influence of Boundary Conditions in the Six-Vertex Model \text{The Influence of Boundary Conditions in the Six-Vertex Model}(2002) @unpublished { artic20, year = {2002}, note = {unpublished preprint}, arxiv = {cond-mat/0205192}, title = {The Influence of Boundary Conditions in the Six-Vertex Model}, author = {Zinn-Justin, Paul} } | |
Inhomogeneous six-vertex model with domain wall boundary
conditions and Bethe Ansatz \text{Inhomogeneous six-vertex model with domain wall boundary
conditions and {B}ethe {A}nsatz}J. Math. Phys. 43 (6) (2002) 3261–3267@article { artic14, arxiv = {nlin.SI/0008030}, mrreviewer = {Katherine A. Seaton}, mrnumber = {MR1902479 (2003g:82021)}, mrclass = {82B20 (82B23)}, coden = {JMAPAQ}, issn = {0022-2488}, pages = {3261--3267}, number = {6}, year = {2002}, volume = {43}, fjournal = {Journal of Mathematical Physics}, journal = {J. Math. Phys.}, title = {Inhomogeneous six-vertex model with domain wall boundary conditions and {B}ethe {A}nsatz}, author = {Korepin, V. and Zinn-Justin, Paul} } | |
Six-vertex model with domain wall boundary conditions and
one-matrix model \text{Six-vertex model with domain wall boundary conditions and
one-matrix model}Phys. Rev. E 62 (3, part A) (2000) 3411–3418@article { artic13, arxiv = {math-ph/0005008}, mrnumber = {MR1788950 (2001g:82037)}, mrclass = {82B20 (82B23)}, coden = {PLEEE8}, issn = {1539-3755}, pages = {3411--3418}, number = {3, part A}, year = {2000}, volume = {62}, fjournal = {Physical Review E. Statistical, Nonlinear, and Soft Matter Physics}, journal = {Phys. Rev. E}, title = {Six-vertex model with domain wall boundary conditions and one-matrix model}, author = {Zinn-Justin, Paul} } | |
Thermodynamic limit of the six-vertex model with domain wall
boundary conditions \text{Thermodynamic limit of the six-vertex model with domain wall
boundary conditions}J. Phys. A 33 (40) (2000) 7053–7066@article { artic12, doi = {10.1088/0305-4470/33/40/304}, arxiv = {cond-mat/0004250}, mrreviewer = {Yvan Velenik}, mrnumber = {MR1792450 (2001h:82018)}, mrclass = {82B20 (82B23)}, coden = {JPHAC5}, issn = {0305-4470}, pages = {7053--7066}, number = {40}, year = {2000}, volume = {33}, fjournal = {Journal of Physics. A. Mathematical and General}, journal = {J. Phys. A}, title = {Thermodynamic limit of the six-vertex model with domain wall boundary conditions}, author = {Korepin, V. and Zinn-Justin, Paul} } | |
Kazhdan–Lusztig polynomials: (1 papers) | |
Path representation of maximal parabolic Kazhdan–Lusztig polynomials \text{Path representation of maximal parabolic {K}azhdan--{L}usztig polynomials}J. Pure Appl. Algebra 216 (11) (2012) 2533–2548@article { artic52, doi = {10.1016/j.jpaa.2012.03.027}, arxiv = {1001.1080}, mrnumber = {2927185}, mrclass = {20C08 (05E15)}, coden = {JPAAA2}, issn = {0022-4049}, pages = {2533--2548}, number = {11}, year = {2012}, volume = {216}, fjournal = {Journal of Pure and Applied Algebra}, journal = {J. Pure Appl. Algebra}, title = {Path representation of maximal parabolic {K}azhdan--{L}usztig polynomials}, author = {Shigechi, K. and Zinn-Justin, Paul} } | |
Integrals over (quantum) groups: (4 papers) | |
Jucys–Murphy elements and Weingarten matrices \text{{J}ucys--{M}urphy elements and {W}eingarten matrices}Lett. Math. Phys. 91 (2) (2010) 119–127@article { artic51, arxiv = {0907.2719}, doi = {10.1007/s11005-009-0365-9}, mrreviewer = {Marius T{\u{a}}rn{\u{a}}uceanu}, mrnumber = {2586868 (2011b:20139)}, mrclass = {20G20 (05E10)}, coden = {LMPHDY}, issn = {0377-9017}, pages = {119--127}, number = {2}, year = {2010}, volume = {91}, fjournal = {Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics}, journal = {Lett. Math. Phys.}, title = {{J}ucys--{M}urphy elements and {W}eingarten matrices}, author = {Zinn-Justin, Paul} } | |
Spectral analysis of the free orthogonal matrix \text{Spectral analysis of the free orthogonal matrix}Int. Math. Res. Not. 17 (2009) 3286–3309@article { artic48, pages = {3286--3309}, volume = {17}, fjournal = {International Mathematics Research Notices}, journal = {Int. Math. Res. Not.}, doi = {10.1093/imrn/rnp054}, year = {2009}, arxiv = {0901.1918}, title = {Spectral analysis of the free orthogonal matrix}, author = {Banica, T. and Collins, B. and Zinn-Justin, Paul} } | |
On some integrals over the U(N) unitary group and
their large N limit \text{On some integrals over the {$U(N)$} unitary group and
their large {$N$} limit}J. Phys. A 36 (12) (2003) 3173–3193@article { artic23, arxiv = {math-ph/0209019}, mrnumber = {MR1986413 (2006c:82029)}, mrclass = {82B41 (15A90 60C05)}, coden = {JPHAC5}, issn = {0305-4470}, pages = {3173--3193}, number = {12}, year = {2003}, volume = {36}, fjournal = {Journal of Physics. A. Mathematical and General}, journal = {J. Phys. A}, note = {special issue on Random Matrix Theory}, title = {On some integrals over the {$U(N)$} unitary group and their large {$N$} limit}, author = {Zinn-Justin, Paul and Zuber, J.-B.} } | |
HCIZ integral and 2D Toda lattice hierarchy \text{H{CIZ} integral and 2{D} {T}oda lattice hierarchy}Nuclear Phys. B 634 (3) (2002) 417–432@article { artic21, arxiv = {math-ph/0202045}, mrreviewer = {Nenad Manojlovi{\'c}}, mrnumber = {MR1912027 (2003f:81113)}, mrclass = {81R12 (37K10 37K60 81T10)}, coden = {NUPBBO}, issn = {0550-3213}, pages = {417--432}, number = {3}, year = {2002}, volume = {634}, fjournal = {Nuclear Physics. B}, journal = {Nuclear Phys. B}, title = {H{CIZ} integral and 2{D} {T}oda lattice hierarchy}, author = {Zinn-Justin, Paul} } | |
Knot Enumeration: (12 papers) | |
Knot theory and matrix integrals \text{Knot theory and matrix integrals}in "The Oxford Handbook of Random Matrix Theory" (2011) @incollection { artic50, arxiv = {1006.1812}, note = {Eds Akemann, Baik and Di Francesco}, booktitle = {The Oxford Handbook of Random Matrix Theory}, year = {2011}, title = {Knot theory and matrix integrals}, author = {Zinn-Justin, P. and Zuber, J.-B.} } | |
Conjectures on the enumeration of alternating links \text{Conjectures on the enumeration of alternating links}in "Physical and numerical models in knot theory" 36 (2005) 597–606@incollection { artic29, mrreviewer = {Goulnara N. Arzhantseva}, mrnumber = {MR2197960 (2006j:57024)}, mrclass = {57M25 (05A16 05C10)}, year = {2005}, publisher = {World Sci. Publ., Singapore}, pages = {597--606}, volume = {36}, series = {Ser. Knots Everything}, booktitle = {Physical and numerical models in knot theory}, title = {Conjectures on the enumeration of alternating links}, author = {Zinn-Justin, Paul} } | |
Matrix integrals and the generation and counting of virtual
tangles and links \text{Matrix integrals and the generation and counting of virtual
tangles and links}J. Knot Theory Ramifications 13 (3) (2004) 325–355@article { artic25, arxiv = {math-ph/0303049}, mrreviewer = {Gw{\'e}na{\"e}l Massuyeau}, mrnumber = {MR2061172 (2005d:57003)}, mrclass = {57M15 (05C30 57M25 81T18)}, issn = {0218-2165}, pages = {325--355}, number = {3}, year = {2004}, volume = {13}, fjournal = {Journal of Knot Theory and its Ramifications}, journal = {J. Knot Theory Ramifications}, title = {Matrix integrals and the generation and counting of virtual tangles and links}, author = {Zinn-Justin, Paul and Zuber, J.-B.} } | |
On the asymptotic number of plane curves and alternating
knots \text{On the asymptotic number of plane curves and alternating
knots}Experiment. Math. 13 (4) (2004) 483–493@article { artic24, arxiv = {math-ph/0304034}, mrreviewer = {Valery A. Liskovets}, mrnumber = {MR2118273 (2006d:05018)}, mrclass = {05A16 (05C30 57M25 83C80)}, issn = {1058-6458}, pages = {483--493}, number = {4}, year = {2004}, volume = {13}, fjournal = {Experimental Mathematics}, journal = {Experiment. Math.}, title = {On the asymptotic number of plane curves and alternating knots}, author = {Schaeffer, G. and Zinn-Justin, Paul} } | |
Matrix models and the enumeration of alternating tangles \text{Matrix models and the enumeration of alternating tangles}Markov Process. Related Fields 9 (2) (2003) 301–310@article { artic18b, mrreviewer = {Sergei K. Lando}, mrnumber = {MR2013665 (2004i:57006)}, mrclass = {57M25 (05C30 82B44)}, issn = {1024-2953}, pages = {301--310}, number = {2}, year = {2003}, volume = {9}, fjournal = {Markov Processes and Related Fields}, journal = {Markov Process. Related Fields}, note = {proceedings of ``Inhomogeneous random systems'' (Cergy-Pontoise, 2002)}, title = {Matrix models and the enumeration of alternating tangles}, author = {Jacobsen, J. and Zinn-Justin, Paul} } | |
The combinatorics of alternating tangles: from theory to
computerized enumeration \text{The combinatorics of alternating tangles: from theory to
computerized enumeration}in "Asymptotic combinatorics with application to mathematical
physics (St. Petersburg, 2001)" 77 (2002) 97–112@incollection { artic18, arxiv = {math-ph/0111011}, mrnumber = {MR1999357 (2004h:57009)}, mrclass = {57M25 (05A15)}, year = {2002}, address = {Dordrecht}, publisher = {Kluwer Acad. Publ.}, pages = {97--112}, volume = {77}, series = {NATO Sci. Ser. II Math. Phys. Chem.}, booktitle = {Asymptotic combinatorics with application to mathematical physics ({S}t. {P}etersburg, 2001)}, title = {The combinatorics of alternating tangles: from theory to computerized enumeration}, author = {Jacobsen, J. and Zinn-Justin, Paul} } | |
The general O(n) quartic matrix model and its
application to counting tangles and links \text{The general {$O(n)$} quartic matrix model and its
application to counting tangles and links}Comm. Math. Phys. 238 (1-2) (2003) 287–304@article { artic17, arxiv = {math-ph/0106005}, mrreviewer = {Richard Kenyon}, mrnumber = {MR1990878 (2004d:57014)}, mrclass = {57M25 (81T99)}, coden = {CMPHAY}, issn = {0010-3616}, pages = {287--304}, number = {1-2}, year = {2003}, volume = {238}, fjournal = {Communications in Mathematical Physics}, journal = {Comm. Math. Phys.}, title = {The general {$O(n)$} quartic matrix model and its application to counting tangles and links}, author = {Zinn-Justin, Paul} } | |
A transfer matrix approach to the enumeration of colored
links \text{A transfer matrix approach to the enumeration of colored
links}J. Knot Theory Ramifications 10 (8) (2001) 1233–1267@article { artic16, arxiv = {math-ph/0104009}, mrnumber = {MR1871228 (2003h:57009)}, mrclass = {57M25 (82B20)}, issn = {0218-2165}, pages = {1233--1267}, number = {8}, year = {2001}, volume = {10}, fjournal = {Journal of Knot Theory and its Ramifications}, journal = {J. Knot Theory Ramifications}, title = {A transfer matrix approach to the enumeration of colored links}, author = {Jacobsen, J. and Zinn-Justin, Paul} } | |
A transfer matrix approach to the enumeration of knots \text{A transfer matrix approach to the enumeration of knots}J. Knot Theory Ramifications 11 (5) (2002) 739–758@article { artic15, arxiv = {math-ph/0102015}, mrreviewer = {Yuanan Diao}, mrnumber = {MR1918811 (2003f:57014)}, mrclass = {57M25}, issn = {0218-2165}, pages = {739--758}, number = {5}, year = {2002}, volume = {11}, fjournal = {Journal of Knot Theory and its Ramifications}, journal = {J. Knot Theory Ramifications}, title = {A transfer matrix approach to the enumeration of knots}, author = {Jacobsen, J. and Zinn-Justin, Paul} } | |
On the counting of colored tangles \text{On the counting of colored tangles}J. Knot Theory Ramifications 9 (8) (2000) 1127–1141@article { artic11, arxiv = {math-ph/0002020}, mrreviewer = {Alexander Zvonkin}, mrnumber = {MR1807611 (2002b:57008)}, mrclass = {57M25 (05C30 15A52 81T18)}, issn = {0218-2165}, pages = {1127--1141}, number = {8}, year = {2000}, volume = {9}, fjournal = {Journal of Knot Theory and its Ramifications}, journal = {J. Knot Theory Ramifications}, title = {On the counting of colored tangles}, author = {Zinn-Justin, Paul and Zuber, J.-B.} } | |
Some matrix integrals related to knots and links \text{Some matrix integrals related to knots and links}in "Random matrix models and their applications" 40 (2001) 421–438@incollection { artic09, arxiv = {math-ph/9910010}, oldnote = {proceedings of the 1999 semester at the MSRI}, mrreviewer = {Saburo Higuchi}, mrnumber = {MR1842796 (2002m:82031)}, mrclass = {82B41 (57M27 60B15 83C27)}, year = {2001}, address = {Cambridge}, publisher = {Cambridge Univ. Press}, pages = {421--438}, volume = {40}, series = {Math. Sci. Res. Inst. Publ.}, booktitle = {Random matrix models and their applications}, title = {Some matrix integrals related to knots and links}, author = {Zinn-Justin, Paul} } | |
Matrix integrals and the counting of tangles and links \text{Matrix integrals and the counting of tangles and links}Discrete Math. 246 (1-3) (2002) 343–360@article { artic08, arxiv = {math-ph/9904019}, mrnumber = {MR1887495 (2003i:57019)}, mrclass = {57M25 (05A15 81Q30 81T18)}, coden = {DSMHA4}, issn = {0012-365X}, pages = {343--360}, number = {1-3}, year = {2002}, volume = {246}, fjournal = {Discrete Mathematics}, journal = {Discrete Math.}, oldnote = {proceedings of ``Formal power series and algebraic combinatorics'' (Barcelona, 1999)}, title = {Matrix integrals and the counting of tangles and links}, author = {Zinn-Justin, Paul and Zuber, J.-B.} } | |
Loop models: (4 papers) | |
A conjectured formula for Fully Packed Loop configurations in a triangle \text{A conjectured formula for {F}ully {P}acked {L}oop configurations in a triangle}Electron. J. Combin. 17 (2010) Research Paper 107@article { artic49, pages = {Research Paper 107}, year = {2010}, volume = {17}, fjournal = {Electronic Journal of Combinatorics}, journal = {Electron. J. Combin.}, arxiv = {0911.4617}, title = {A conjectured formula for {F}ully {P}acked {L}oop configurations in a triangle}, author = {Zinn-Justin, Paul} } | |
Determinant formulae for some tiling problems and application
to fully packed loops \text{Determinant formulae for some tiling problems and application
to fully packed loops}Ann. Inst. Fourier (Grenoble) 55 (6) (2005) 2025–2050@article { artic30, arxiv = {math-ph/0410002}, mrreviewer = {David M. Bressoud}, mrnumber = {MR2187944 (2007f:05037)}, mrclass = {05B45 (05A19 05E05 52C20 82B20)}, coden = {AIFUA7}, issn = {0373-0956}, pages = {2025--2050}, number = {6}, year = {2005}, volume = {55}, fjournal = {Universit\'e de Grenoble. Annales de l'Institut Fourier}, journal = {Ann. Inst. Fourier (Grenoble)}, title = {Determinant formulae for some tiling problems and application to fully packed loops}, author = {Di Francesco, P. and Zinn-Justin, Paul and Zuber, J.-B.} } | |
Algebraic Bethe Ansatz for the FPL^2 model \text{Algebraic {B}ethe {A}nsatz for the {FPL$^2$} model}J. Phys. A 37 (29) (2004) 7213–7225@article { artic28, doi = {10.1088/0305-4470/37/29/004}, arxiv = {math-ph/0402008}, mrreviewer = {Yao Zhong Zhang}, mrnumber = {MR2078954 (2005e:82014)}, mrclass = {82B20 (81R50 82B23)}, coden = {JPHAC5}, issn = {0305-4470}, pages = {7213--7225}, number = {29}, year = {2004}, volume = {37}, fjournal = {Journal of Physics. A. Mathematical and General}, journal = {J. Phys. A}, title = {Algebraic {B}ethe {A}nsatz for the {FPL$^2$} model}, author = {Jacobsen, J. and Zinn-Justin, Paul} } | |
A bijection between classes of fully packed loops and plane
partitions \text{A bijection between classes of fully packed loops and plane
partitions}Electron. J. Combin. 11 (1) (2004) Research Paper 64, 11 pp@article { artic27, arxiv = {math/0311220}, mrreviewer = {Christian Krattenthaler}, mrnumber = {MR2097330 (2006d:05021)}, mrclass = {05A19}, issn = {1077-8926}, pages = {Research Paper 64, 11 pp}, number = {1}, year = {2004}, volume = {11}, fjournal = {Electronic Journal of Combinatorics}, journal = {Electron. J. Combin.}, title = {A bijection between classes of fully packed loops and plane partitions}, author = {Di Francesco, P. and Zinn-Justin, Paul and Zuber, J.-B.} } | |
Percolation: (2 papers) | |
Monochromatic path crossing exponents and graph connectivity in 2D percolation \text{Monochromatic path crossing exponents and graph connectivity in 2D percolation}Phys. Rev. E 66 (R) (2002) 055102@article { artic22, arxiv = {cond-mat/0207063}, pages = {055102}, number = {R}, year = {2002}, volume = {66}, journal = {Phys. Rev. E}, title = {Monochromatic path crossing exponents and graph connectivity in 2D percolation}, author = {Jacobsen, J. and Zinn-Justin, Paul} } | |
A transfer matrix for the backbone exponent of two-dimensional
percolation \text{A transfer matrix for the backbone exponent of two-dimensional
percolation}J. Phys. A 35 (9) (2002) 2131–2144@article { artic19, arxiv = {cond-mat/0111374}, mrnumber = {MR1908712 (2003e:82033)}, mrclass = {82B43}, coden = {JPHAC5}, issn = {0305-4470}, pages = {2131--2144}, number = {9}, year = {2002}, volume = {35}, fjournal = {Journal of Physics. A. Mathematical and General}, journal = {J. Phys. A}, title = {A transfer matrix for the backbone exponent of two-dimensional percolation}, author = {Jacobsen, J. and Zinn-Justin, Paul} } |