The multivariate arithmetic Tutte polynomial
2012 (English)In: Discrete Mathematics & Theoretical Computer Science, ISSN 1462-7264, E-ISSN 1365-8050, 661-672 p.Article in journal (Refereed) Published
We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two. We provide a generalized Fortuin-Kasteleyn representation for representable arithmetic matroids, with applications to arithmetic colorings and flows. We give a new proof of the positivity of the coefficients of the arithmetic Tutte polynomial in the more general framework of pseudo-arithmetic matroids. In the case of a representable arithmetic matroid, we provide a geometric interpretation of the coefficients of the arithmetic Tutte polynomial.
Place, publisher, year, edition, pages
2012. 661-672 p.
Abelian groups, Arithmetic matroids, Chromatic polynomial, Matroids, Potts model, Tutte polynomial
Mathematics Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-144779ScopusID: 2-s2.0-84887518992OAI: oai:DiVA.org:kth-144779DiVA: diva2:715368
24th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2012; Nagoya; Japan; 30 July 2012 through 3 August 2012
QC 201405052014-05-052014-04-292014-05-05Bibliographically approved