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arXiv:0803.1477 [math.CO]AbstractReferencesReviewsResources

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

Alexander D. Scott, Alan D. Sokal

Published 2008-03-10, updated 2009-02-17Version 2

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.

Comments: LaTeX2e, 39 pages. Dedicated to the memory of Pierre Leroux. Version 2 includes a new Appendix presenting a generalization of Mobius inversion on the partition lattice
Journal: Seminaire Lotharingien de Combinatoire 61A, article 61Ae (2009)
Categories: math.CO, math-ph, math.MP
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