352 research outputs found
Proof of two conjectures of Zuber on fully packed loop configurations
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.Comment: 20 pages; AmS-LaTe
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