Grid graphs, Gorenstein polytopes, and domino stackings
Matthias Beck, Christian Haase, and Steven V. Sam
TL;DR
This paper explores the properties of perfect matching polytopes in grid graphs related to domino tilings, introduces domino stackings, and investigates when these polytopes are Gorenstein, combining graph theory and polyhedral geometry.
Contribution
It introduces the concept of domino stackings and studies Gorenstein properties of perfect matching polytopes in grid graphs, with new results and open questions.
Findings
Characterization of Gorenstein perfect matching polytopes
Introduction of domino stackings and their properties
Open questions on polytope Gorenstein conditions
Abstract
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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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models