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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Log-concavity of asymptotic multigraded Hilbert series
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by Adam McCabe and Gregory G. Smith PDF
Proc. Amer. Math. Soc. 141 (2013), 1883-1892 Request permission

Abstract:

We study the linear map sending the numerator of the rational function representing the Hilbert series of a module to that of its $r$-th Veronese submodule. We show that the asymptotic behaviour as $r$ tends to infinity depends on the multidegree of the module and the underlying positively multigraded polynomial ring. More importantly, we give a polyhedral description for the asymptotic polynomial and prove that the coefficients are log-concave.
References
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Additional Information
  • Adam McCabe
  • Affiliation: 35 Summerhill Road, Holland Landing, Ontario, L9N 1C6, Canada
  • Email: adam.r.mccabe@gmail.com
  • Gregory G. Smith
  • Affiliation: Department of Mathematics & Statistics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
  • MR Author ID: 622959
  • Email: ggsmith@mast.queensu.ca
  • Received by editor(s): September 20, 2011
  • Published electronically: December 20, 2012
  • Communicated by: Irena Peeva
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 1883-1892
  • MSC (2010): Primary 05E40, 13D40, 52B20
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11808-8
  • MathSciNet review: 3034415