Schur function identities and the number of perfect matchings of holey Aztec rectangles
Christian Krattenthaler
Abstract
We compute the number of perfect matchings of an M× 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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