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. © 2012 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.

The multivariate arithmetic Tutte polynomial

Moci L
2012

Abstract

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. © 2012 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.
2012
24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
661
672
Branden P; Moci L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/676846
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