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Journal of Statistical Physics

, Volume 142, Issue 4, pp 879–897 | Cite as

Resistance Scaling and the Number of Spanning Trees in Self-Similar Lattices

  • Elmar TeuflEmail author
  • Stephan Wagner
Article

Abstract

We consider the problem of enumerating spanning trees in self-similar lattices, motivated by recent work of Chang, Chen and Yang, who determined explicit formulae in the case of Sierpiński graphs and some of their generalizations. The aim of this note is to show that their results hold in more generality and that there is a strong relation between this enumeration problem and resistance scaling on self-similar lattices.

Keywords

Self-similar lattices Electrical networks Resistance scaling Spanning trees 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität TübingenTübingenGermany
  2. 2.Department of Mathematical SciencesStellenbosch UniversityMatielandSouth Africa

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