This material has been published in
J. Combin. Theory Ser. A 108 (2004), 123-146,
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Proof of two conjectures of Zuber on fully packed loop configurations
Two conjectures of Zuber
[``On the counting
of fully packed loops
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
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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