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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A Tutte polynomial for toric arrangements
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by Luca Moci PDF
Trans. Amer. Math. Soc. 364 (2012), 1067-1088 Request permission

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
  • Received by editor(s): June 30, 2010
  • Received by editor(s) in revised form: October 14, 2010
  • Published electronically: September 15, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 1067-1088
  • MSC (2010): Primary 52C35; Secondary 05B35, 20G20
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05491-7
  • MathSciNet review: 2846363