Skip to Main content Skip to Navigation
Conference papers

Zonotopes, toric arrangements, and generalized Tutte polynomials

Abstract : 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.
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download

https://hal.inria.fr/hal-01186307
Contributor : Coordination Episciences Iam <>
Submitted on : Monday, August 24, 2015 - 3:49:18 PM
Last modification on : Thursday, June 18, 2020 - 12:46:02 PM
Long-term archiving on: : Wednesday, November 25, 2015 - 6:09:20 PM

File

dmAN0125.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01186307, version 1

Collections

Citation

Luca Moci. Zonotopes, toric arrangements, and generalized Tutte polynomials. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.413-424. ⟨hal-01186307⟩

Share

Metrics

Record views

283

Files downloads

823