A Bijection between classes of Fully Packed Loops and Plane Partitions

P. Di Francesco, P. Zinn-Justin, J. -B. Zuber

Published 2003-11-13Version 1

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.