A Bijection between classes of Fully Packed Loops and Plane Partitions

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

Electronic Journal of Combinatories 11 (2004) R64

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.

  • 1. Service de Physique Théorique (SPhT),
    CNRS : URA2306 – CEA : DSM/SPHT
  • 2. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
    CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot