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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
2014 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 366, no 10, 5523-5540 p.Article in journal (Refereed) Published
Abstract [en]

We introduce an arithmetic version of the multivariate Tutte polynomial and a quasi-polynomial that interpolates between the two. A generalized Fortuin-Kasteleyn representation with applications to arithmetic colorings and flows is obtained. We give a new and more general proof of the positivity of the coefficients of the arithmetic Tutte polynomial and (in the representable case) a geometrical interpretation of them.

Place, publisher, year, edition, pages
2014. Vol. 366, no 10, 5523-5540 p.
Keyword [en]
Tutte polynomial, multivariate Tutte polynomial, Potts model, toric arrangement, chromatic polynomial, matroid, arithmetic matroid, abelian group, quasi-polynomial
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-158844DOI: 10.1090/S0002-9947-2014-06092-3ISI: 000344826100017Scopus ID: 2-s2.0-84924785538OAI: oai:DiVA.org:kth-158844DiVA: diva2:782697
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20150122

Available from: 2015-01-22 Created: 2015-01-12 Last updated: 2017-12-05Bibliographically approved

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Bränden, Petter

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