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

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

1997-11-26

arxiv.org/abs/math/9712204v2

in: "q-Series from a Contemporary Perspective," M. E. H. Ismail, D. Stanton, eds., Contemporary Math., vol. 254, Amer. Math. S

Mathematics

Combinatorics

15 pages, AmS-TeX

Scientific paper

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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