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