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Schur function identities and the number of perfect matchings of holey Aztec rectangles

Christian Krattenthaler
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Abstract

We compute the number of perfect matchings of an $M\times N$ 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 paths.

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Christian Krattenthaler. 1997-12-21. Schur function identities and the number of perfect matchings of holey Aztec rectangles. https://arxiv.org/abs/math/9712204

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