On the number of fully packed loop configurations with a fixed associated matching

Fabrizio Caselli , Christian Krattenthaler (1) , Bodo Lass (1) , Philippe Nadeau (2)

1 ICJ - Institut Camille Jordan
2 LRI - Laboratoire de Recherche en Informatique

We show that the number of fully packed loop configurations corresponding to a matching with $m$ nested arches is polynomial in $m$ if $m$ is large enough, thus essentially proving two conjectures by Zuber [Electronic J. Combin. 11 (2004), Article #R13].

Domaines: Combinatoire [math.CO]; Physique mathématique [math-ph]

Fabrizio Caselli, Christian Krattenthaler, Bodo Lass, Philippe Nadeau. On the number of fully packed loop configurations with a fixed associated matching. The Electronic Journal of Combinatorics, 2005, 11 numéro 1, pp.#R16. ⟨hal-00129292⟩