Evènement pour le groupe Combinatoire Énumérative et Algébrique
|Date|| 2012-06-22 10:45-11:45|
|Titre||Spanning trees, lattice Green functions and Mahler measures |
|Résumé||On regular lattices the number of spanning trees grows exponentially, characterised by a constant known as the spanning tree constant. This constant is known for two dimensional lattices, but not for three dimensional lattices (with one exception). By recasting the definition in terms of the logarithmic Mahler measure of a Laurent polynomial, we can make use of recently proved results for Mahler measures to find the spanning tree constant for the four regular three-dimensional lattices. Further, by generalizing the spanning tree constant to what we call a spanning tree generating function (STGF), we relate this to the lattice Green function (LGF), and comparing results between the LGF and the STGF gives possibly new hypergeometric function identities.
Joint work with Mathew Rogers (Illinois, USA). |
|Orateur||Tony Guttmann |
|Url||The University of Melbourne, Australia |
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