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On the Entropy of Spanning Trees on a Large Triangular Lattice

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Abstract

The double integral representing the entropy Stri of spanning trees on a large triangular lattice is evaluated using two different methods, one algebraic and one graphical. Both methods lead to the same result

$$ S_{\rm tri} = (4 \pi^2)^{-1} \int_{0}^{2 \pi} d \theta \int^{2 \pi}_{0}d \phi \ln {[}6-2 \cos \theta-2 \cos \phi-2 \cos (\theta + \phi){]} = (3 \sqrt{3}/\pi)(1-5^{-2} + 7^{-2} - 11^{-2} + 13^{-2}-\ldots).$$

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Authors and Affiliations

  1. Department of Physics, Clarkson University, Potsdam, New York, 13699

    M. L. Glasser

  2. Department of Physics, Northeastern University, Boston, Massachusetts, 02115

    F. Y. Wu

Authors
  1. M. L. Glasser
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  2. F. Y. Wu
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Correspondence to M. L. Glasser.

Additional information

2000 Mathematics Subject Classification: Primary—05A16, 33B30, 82B20

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Glasser, M.L., Wu, F.Y. On the Entropy of Spanning Trees on a Large Triangular Lattice. Ramanujan J 10, 205–214 (2005). https://doi.org/10.1007/s11139-005-4847-9

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  • DOI: https://doi.org/10.1007/s11139-005-4847-9

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