Luca Moci

Zonotopes, toric arrangements, and generalized Tutte polynomials
dmtcs:2878 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2010,
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)

https://doi.org/10.46298/dmtcs.2878
Zonotopes, toric arrangements, and generalized Tutte polynomials
Authors: Luca Moci ^{1}
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Luca Moci
1 Dipartimento di Matematica [Roma TRE]
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 deletionrestriction 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 DahmenMicchelli space, while $M(x,1)$ computes the volume and the number of integral points of the associated zonotope.
Moci, Luca, 000000016744515; Settepanella, Simona, 2011, The Homotopy Type Of Toric Arrangements, Journal Of Pure And Applied Algebra, 215, 8, pp. 19801989, 10.1016/j.jpaa.2010.11.008.