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

Details 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

2005-02-17

arxiv.org/abs/math/0502392v2

Electronic J. Combin. 11(2) (2005), Article #R16, 43 pp

Mathematics

Combinatorics

AnS-LaTeX, 43 pages; Journal version

Scientific paper

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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