A Tutte polynomial for toric arrangements

Moci, Luca

doi:10.1090/S0002-9947-2011-05491-7

A Tutte polynomial for toric arrangements
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Trans. Amer. Math. Soc. 364 (2012), 1067-1088 Request permission

Abstract:

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 recursion and has positive coefficients. The characteristic polynomial and the Poincaré 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 integer points of the associated zonotope.

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