A Bijection between classes of Fully Packed Loops and Plane Partitions

P. Di Francesco (1) , Paul Zinn-Justin (2) , J. -B. Zuber (1)

1 SPhT - Service de Physique Théorique
2 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Domaines: Combinatoire [math.CO]

P. Di Francesco, Paul Zinn-Justin, J. -B. Zuber. A Bijection between classes of Fully Packed Loops and Plane Partitions. The Electronic Journal of Combinatorics, 2004, 11, pp.R64. ⟨hal-00004275⟩