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

Christian Krattenthaler

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

Combinatorics 2007-05-23 v2

Authors: Christian Krattenthaler

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.

Keywords

perfect matchings aztec rectangle schur functions nonintersecting lattice paths enumeration

Cite

@article{arxiv.math/9712204,
  title  = {Schur function identities and the number of perfect matchings of holey Aztec rectangles},
  author = {Christian Krattenthaler},
  journal= {arXiv preprint arXiv:math/9712204},
  year   = {2007}
}

Comments

15 pages, AmS-TeX

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