Some variants of the exponential formula, with application to the multivariate Tutte polynomial (alias Potts model)

Details Some variants of the exponential formula, with application to the multivariate Tutte polynomial (alias Potts model) Some variants of the exponential formula, with application to the multivariate Tutte polynomial (alias Potts model)

2008-03-10

arxiv.org/abs/0803.1477v2

Seminaire Lotharingien de Combinatoire 61A, article 61Ae (2009)

Mathematics

Combinatorics

LaTeX2e, 39 pages. Dedicated to the memory of Pierre Leroux. Version 2 includes a new Appendix presenting a generalization of

Scientific paper

We prove some variants of the exponential formula and apply them to the multivariate Tutte polynomials (also known as Potts-model partition functions) of graphs. We also prove some further identities for the multivariate Tutte polynomial, which generalize an identity for counting connected graphs found by Riordan, Nijenhuis, Wilf and Kreweras and in more general form by Leroux and Gessel, and an identity for the inversion enumerator of trees found by Mallows, Riordan and Kreweras. Finally, we prove a generalization of Mobius inversion on the partition lattice.

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