Last updated: 02/2004

Fully Packed Loops and Plane Partitions

This is the frontpage for a little site developed to show explicitly the bijection described in the paper A Bijection between classes of Fully Packed Loops and Plane Partitions by P. Di Francesco, P. Zinn-Justin and J.-B. Zuber.

More precisely this is a bijection between (i) Plane partitions in a box of size a x b x c, and (ii) Fully Packed Loop configuration with fixed connectivity pattern of a special form: three bundles of a, b, c arches.

The simplest way to use this site is to check out the gallery. You will find samples of FPL configurations. By clicking on them you will get the full set of FPL configurations with the same connectivity pattern and the corresponding plane partitions and non-crossings paths.

You can also access the editor. This will allow you to draw yourself the FPL configuration you want (with 3 series of arches -- if you provide another connectivity pattern the result is unpredictable and may turn your computer into a washing machine), possibly rotate it using Wieland's rotation, and to ask for the bijection (either pre-calculated or calculated in real time if the size is sufficiently small).

Hopefully this site is self-explanatory... Enjoy.