This material has been published in J. Combin. Theory Ser. A 108 (2004), 123-146, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier B.V. This material may not be copied or reposted without explicit permission.

Fabrizio Caselli and Christian Krattenthaler

Proof of two conjectures of Zuber on fully packed loop configurations

(20 pages)

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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