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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96433We 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].AnS-LaTeX, 43 pages; Journal versionCombinatoricsMathematical PhysicsPrimary 05A15; Secondary 05B45 05E05 05E10 82B23On the number of fully packed loop configurations with a fixed associated matchingtext