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

zbMath1283.05138arXiv0803.1477MaRDI QIDQ846046

Alan D. Sokal, Alexander D. Scott

Publication date: 29 January 2010

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.1477

zbMATH Keywords

graphgenerating functionMöbius inversionPotts modelTutte polynomialexponential formulacomplete graphconnected componentpartition latticeconvolution familyAbel's binomial identityChu-Vandermonde convolutioninversion enumerator for treesRothe's identitysequence of binomial type

Mathematics Subject Classification ID

Graph polynomials (05C31) Exact enumeration problems, generating functions (05A15) Partitions of sets (05A18) Combinatorial identities, bijective combinatorics (05A19) Combinatorics of partially ordered sets (06A07) Enumeration in graph theory (05C30) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Graph theory (05C99)

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The bipermutahedron ⋮ The partition-frequency enumeration matrix ⋮ Benjamini-Schramm continuity of root moments of graph polynomials ⋮ Total positivity of some polynomial matrices that enumerate labeled trees and forests. I: Forests of rooted labeled trees ⋮ Lagrange inversion theorem for Dirichlet series ⋮ How To Generalize (and Not To Generalize) the Chu–Vandermonde Identity

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