Proof of two conjectures of Zuber on fully packed loop configurations

2003/12/11 by F. Caselli, C. Krattenthaler
Mathematics · Physics and Astronomy · #math.CO #cond-mat.stat-mech #math-ph #math.MP #msc:05A15 #msc:05B45 #msc:05E05 #msc:05E10 #msc:82B23

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published as J. Combin. Theory Ser. A 108 (2004), 123-146. · 20 pages; AmS-LaTeX

arxiv created 2003/12/11 · arxiv updated 2009/12/01

Abstract

Two conjectures of Zuber [``On the counting of fully packed loops configurations. Some new conjectures,'' preprint] on the enumeration of configurations in the fully packed loop model on the square grid with periodic boundary conditions, which have a prescribed linkage pattern, are proved. Following an idea of de Gier [``Loops, matchings and alternating-sign matrices,'' Discrete Math., to appear], the proofs are based on bijections between such fully packed loop configurations and rhombus tilings, and the hook-content formula for semistandard tableaux.

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