Spanning tree generating functions and Mahler measures

  title={Spanning tree generating functions and Mahler measures},
  author={Anthony J. Guttmann and Mathew Rogers},
  journal={arXiv: Mathematical Physics},
We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form… 
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  • R. Lyons
  • Mathematics, Computer Science
    Combinatorics, Probability and Computing
  • 2005
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