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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A Tutte polynomial for toric arrangements


Author: Luca Moci
Journal: Trans. Amer. Math. Soc. 364 (2012), 1067-1088
MSC (2010): Primary 52C35; Secondary 05B35, 20G20
Published electronically: September 15, 2011
MathSciNet review: 2846363
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Abstract: 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.


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Additional Information

Luca Moci
Affiliation: Dipartimento di Matematica, “Guido Castelnuovo” Sapienza Universitá di Roma, Piazzale Aldo Moro, 5, 00185, Roma, Italy

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05491-7
PII: S 0002-9947(2011)05491-7
Received by editor(s): June 30, 2010
Received by editor(s) in revised form: October 14, 2010
Published electronically: September 15, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.