Brändèn, Petter and Moci, Luca - The multivariate arithmetic Tutte polynomial

dmtcs:3072 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
The multivariate arithmetic Tutte polynomial

Authors: Brändèn, Petter and Moci, Luca

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: Potts model, Tutte polynomial, chromatic polynomial, matroids, arithmetic matroids, abelian groups.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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