Grid Graphs, Gorenstein Polytopes, and Domino Stackings

نویسندگان

  • Matthias Beck
  • Christian Haase
  • Steven V. Sam
چکیده

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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منابع مشابه

Lattice Polytopes in Algebra ,

[1] Victor V. Batyrev and Benjamin Nill. Multiples of lattice polytopes without interior lattice points. Moscow Mathematical Journal 7:195–207, 2007. [2] Victor V. Batyrev, Benjamin Nill. Combinatorial aspects of mirror symmetry. Contemporary Mathematics, 452:35–66, 2008. [3] Barbara Baumeister, Christian Haase, Benjamin Nill and Andreas Paffenholz. On permutation polytopes. Advances in Mathema...

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عنوان ژورنال:
  • Graphs and Combinatorics

دوره 25  شماره 

صفحات  -

تاریخ انتشار 2009