A bijection between classes of fully packed loops and plane partitions (Q1883684)

Summary: It has recently been observed empirically that the number of fully packed loop 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 fully packed loops and plane partitions.