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Graphs and Combinatorics

, 25:409 | Cite as

Grid Graphs, Gorenstein Polytopes, and Domino Stackings

  • Matthias Beck
  • Christian Haase
  • Steven V Sam
Article
  • 66 Downloads

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.

Keywords

magic labellings domino tilings perfect matching polytopes rational functions grid graphs Gorenstein polytopes Ehrhart polynomials recurrence relations reciprocity theorems 

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Copyright information

© Springer 2009

Authors and Affiliations

  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA
  2. 2.Fachbereich Mathematik und InformatikFreie Universität BerlinBerlinGermany
  3. 3.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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