Grid graphs, Gorenstein polytopes, and domino stackings

Details Grid graphs, Gorenstein polytopes, and domino stackings Grid graphs, Gorenstein polytopes, and domino stackings

2007-11-26

arxiv.org/abs/0711.4151v2

Graphs Combin. 25 (2009), 409-426

Mathematics

Combinatorics

14 pages, 6 figures, uses graphs package

Scientific paper

10.1007/s00373-005-0858-y

We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching polytopes, and we present some of their properties, in particular, when these polytopes are Gorenstein. We also introduce the notion of domino stackings and present some results and several open questions. Our techniques use results from graph theory, polyhedral geometry, and enumerative combinatorics.

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