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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 polynomialsConference paper

Authors: Luca Moci ORCID1

  • 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 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.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Tutte polynomial,zonotope,integral points,toric arrangement,characteristic polynomial,Dahmen-Micchelli,partition function,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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