A Bijection between classes of Fully Packed Loops and Plane Partitions

2003/11/13 by Philippe Di Francesco, P. Di Francesco, Di Francesco, P. +6
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Mathematics and Applications #cond-mat.stat-mech #graph theory and CDMA systems #math-ph #math.CO #math.MP

paper · pdf · doi:10.48550/arxiv.math/0311220

arxiv created 2003/11/13 · arxiv updated 2009/12/01

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.

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