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

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.

15 pages, AmS-TeX