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

1997/12/21 by Christian Krattenthaler · 2 citations
Mathematics · #math.CO #msc:05A15 #msc:05A16 #msc:05A17 #msc:05A19 #msc:05B45 #msc:33C20 #msc:52C20

paper · pdf

published as in: "q-Series from a Contemporary Perspective," M. E. H. Ismail, D. Stanton, eds., Contemporary Math., vol. 254, Amer. Math. Soc., Providence, R.I., 2000, pp. 335-350. · 15 pages, AmS-TeX

arxiv created 1997/12/21 · arxiv updated 2009/11/30

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.

Cited by

• Round Aztec windows, a dual of the Aztec diamond theorem and a curious symmetry of the correlation of diagonal slits
• A short combinatorial proof of Di Francesco's conjecture on Aztec triangles

Related

• On the numbers of perfect matchings of trimmed Aztec rectangles
• Perfect matchings and perfect powers
• Generating function of the tilings of Aztec rectangle with holes
• A short combinatorial proof of Di Francesco's conjecture on Aztec triangles
• Propp's benzels and Lai's nearly symmetric hexagons with holes