This material has been published in
"q-Series from a Contemporary Perspective," M. E. H. Ismail,
eds., Contemporary Math., vol. 254, Amer. Math. Soc., Providence,
R.I., 2000, pp. 335-350,
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Schur function identities and the number of perfect matchings of
holey Aztec rectangles
We compute the number of perfect matchings of an MxN Aztec
rectangle where |N-M| vertices have been removed along a line. A
particular case solves a problem posed by Propp.
Our enumeration results follow from
certain identities for Schur functions, which
are established by the combinatorics of nonintersecting lattice path.
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