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The multivariate arithmetic Tutte polynomial
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-1055-1474
2012 (English)In: Discrete Mathematics & Theoretical Computer Science, ISSN 1462-7264, E-ISSN 1365-8050, 661-672 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
Abelian groups, Arithmetic matroids, Chromatic polynomial, Matroids, Potts model, Tutte polynomial
National Category
Mathematics Computer and Information Science
URN: urn:nbn:se:kth:diva-144779ScopusID: 2-s2.0-84887518992OAI: diva2:715368
24th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2012; Nagoya; Japan; 30 July 2012 through 3 August 2012

QC 20140505

Available from: 2014-05-05 Created: 2014-04-29 Last updated: 2014-05-05Bibliographically approved

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Brändén, Petter
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