A Bijection Between Classes of Fully Packed Loops and Plane Partitions

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 $a\times b \times c$. In this note, this result is proved by constructing explicitly the bijection between these FPL and plane partitions.