A Tutte Polynomial for Toric Arrangements
نویسندگان
چکیده
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. Ad Alessandro Pucci, che ha ripreso in mano il timone della propria vita.
منابع مشابه
Zonotopes, toric arrangements, and generalized Tutte polynomials
We introduce a multiplicity Tutte polynomial M(x, y), which generalizes the ordinary one and has 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 Poincaré polynomial of a toric arrangement are shown to be specializations of the associated polynomial M(x, y), li...
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