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The energy and spanning trees of the Aztec diamonds

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Volume
311
Issue
1
Identifiers
DOI: 10.1016/j.disc.2010.09.018
Keywords
  • Energy
  • Spanning Tree
  • Aztec Diamond
  • Toroidal Boundary Condition
Disciplines
  • Mathematics

Abstract

Abstract The Aztec diamond was extensively studied in both graph theory and statistical physics. Knuth obtained a formula of the number of spanning trees of the Aztec diamond with the constrained boundary condition, which solved a conjecture posed by Stanley in 1994. In this paper, We give the formulae of the energy and the number of spanning trees of the Aztec diamond with the toroidal boundary condition.

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