Zonotopes, toric arrangements, and generalized Tutte polynomials
نویسنده
چکیده
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), 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. Résumé. On introduit un polynôme de Tutte avec multiplicité M(x, y), qui généralise le polynôme de Tutte ordinaire et a des applications aux zonotopes et aux arrangements toriques. Nous prouvons que M(x, y) satisfait une récurrence de “deletion-restriction” et a des coefficients positifs. Le polynôme caractéristique et le polynôme de Poincaré d’un arrangement torique sont des spécialisations du polynôme associé M(x, y), de même que les polynômes correspondants pour un arrangement d’hyperplans sont des spécialisations du polynôme de Tutte ordinaire. En outre, M(1, y) est la série de Hilbert de l’espace discret de Dahmen-Micchelli associé, et M(x, 1) calcule le volume et le nombre de points entiers du zonotope associé.
منابع مشابه
A Tutte Polynomial for Toric Arrangements
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 fo...
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