A Bijection between classes of Fully Packed Loops and Plane Partitions
Combinatorics
2007-05-23 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a x b x c. In this note, this result is proved by constructing explicitly the bijection between these FPL and plane partitions.
Cite
@article{arxiv.math/0311220,
title = {A Bijection between classes of Fully Packed Loops and Plane Partitions},
author = {P. Di Francesco and P. Zinn-Justin and J. -B. Zuber},
journal= {arXiv preprint arXiv:math/0311220},
year = {2007}
}