Elsevier

Discrete Mathematics

Volume 311, Issue 1, 6 January 2011, Pages 38-44
Discrete Mathematics

The energy and spanning trees of the Aztec diamonds

https://doi.org/10.1016/j.disc.2010.09.018Get rights and content
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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.

Keywords

Energy
Spanning tree
Aztec diamond
Toroidal boundary condition

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