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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Arithmetical rank of toric ideals associated to graphs
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by Anargyros Katsabekis PDF
Proc. Amer. Math. Soc. 138 (2010), 3111-3123 Request permission

Abstract:

Let $I_{G} \subset K[x_{1},\ldots ,x_{m}]$ be the toric ideal associated to a finite graph $G$. In this paper we study the binomial arithmetical rank and the $G$-homogeneous arithmetical rank of $I_G$ in 2 cases:

  1. $G$ is bipartite,

  2. $I_G$ is generated by quadratic binomials.

In both cases we prove that the binomial arithmetical rank and the $G$-homogeneous arithmetical rank coincide with the minimal number of generators of $I_G$.

References
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Additional Information
  • Anargyros Katsabekis
  • Affiliation: Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece
  • Email: katsabek@aegean.gr
  • Received by editor(s): December 16, 2008
  • Received by editor(s) in revised form: December 16, 2009
  • Published electronically: May 26, 2010
  • Communicated by: Bernd Ulrich
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 3111-3123
  • MSC (2010): Primary 14M25, 13F20, 05C99
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10335-0
  • MathSciNet review: 2653936