A Tutte polynomial for toric arrangements

By Luca Moci. 2009

100 citations recorded by the source corpus.

We introduce a multiplicity Tutte polynomial M(x,y), with applications to zonotopes and toric arrangements. We prove that M(x,y) satisfies a deletion-restriction recurrence and has positive coefficients. The characteristic polynomial and the Poincare' polynomial of a toric arrangement are shown to be specializations of the associated polynomial M(x,y), likewise the corresponding polynomials for a hyperplane arrangement are specializations of the ordinary Tutte polynomial. Furthermore, M(1,y) is the Hilbert series of the related discrete Dahmen-Micchelli space, while M(x,1) computes the volume and the number of integral points of the associated zonotope.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21917a3420d029fc7508dd72b2051cf20d7b8ac3

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In Algebra and Number Theory

1. Alex Fink
2. Petter Brand'en
3. Luca Moci
4. Federico Ardila
5. Eric Katz

In Discrete Mathematics and Combinatorics

1. Alex Fink
2. Petter Brand'en
3. Luca Moci
4. Julius Borcea
5. Federico Ardila
6. Eric Katz

In Mathematical Physics

1. Alex Fink
2. Petter Brand'en
3. Luca Moci
4. Julius Borcea

Citations in the corpus

• The multivariate arithmetic Tutte polynomial (2012, background): “Dans le cas d’un matroı̈de arithmétique représentable, nous proposons une interpretation geometrique des coefficients du polynôme de Tutte arithmetique.”
• Matroids over a ring (2012, background): “In the years since 1935, when Whitney first introduced matroids, a number of enriched variants thereof have arisen, among them oriented matroids [2], valuated matroids [8], complex matroids [1], and (quasi-) arithmetic matroids [13, 5].”