On the Number of Fully Packed Loop Configurations with a Fixed Associated Matching

F. Caselli, C. Krattenthaler, B. Lass, P. Nadeau


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(1) (2004), Article #R13].

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