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

Bodo Lass (Universit\'e Lyon-I); Christian Krattenthaler; Fabrizio Caselli; Philippe Nadeau (Universit\'e Paris Sud)

arxiv: math/0502392 · v2 · submitted 2005-02-17 · 🧮 math.CO · math-ph· math.MP

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

Fabrizio Caselli , Christian Krattenthaler , Bodo Lass (Universit\'e Lyon-I) , Philippe Nadeau (Universit\'e Paris Sud) This is my paper

classification 🧮 math.CO math-phmath.MP

keywords configurationsfullyloopmatchingnumberpackedarchesarticle

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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].

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

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