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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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Two way subtable sum problems and quadratic Gröbner bases
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by Hidefumi Ohsugi and Takayuki Hibi PDF
Proc. Amer. Math. Soc. 137 (2009), 1539-1542 Request permission


Hara, Takemura and Yoshida discussed toric ideals arising from two way subtable sum problems and showed that these toric ideals are generated by quadratic binomials if and only if the subtables are either diagonal or triangular. In the present paper, we show that if the subtables are either diagonal or triangular, then their toric ideals possess quadratic Gröbner bases.
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  • H. Hara, A. Takemura and R. Yoshida, Markov bases for two-way subtable sum problems, arXiv:math.CO/0708.2312v1, 2007.
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  • H. Ohsugi and T. Hibi, Toric ideals arising from contingency tables, in Commutative Algebra and Combinatorics, Ramanujan Mathematical Society Lecture Notes Series, Vol. 4, Ramanujan Mathematical Society, Mysore, India, 2007, pp. 91–115.
  • Bernd Sturmfels, Gröbner bases and convex polytopes, University Lecture Series, vol. 8, American Mathematical Society, Providence, RI, 1996. MR 1363949, DOI 10.1090/ulect/008
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Additional Information
  • Hidefumi Ohsugi
  • Affiliation: Department of Mathematics, College of Science, Rikkyo University, Toshima, Tokyo 171-8501, Japan
  • Email:
  • Takayuki Hibi
  • Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
  • MR Author ID: 219759
  • Email:
  • Received by editor(s): December 2, 2007
  • Received by editor(s) in revised form: April 29, 2008, and June 13, 2008
  • Published electronically: December 5, 2008
  • Communicated by: Bernd Ulrich
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1539-1542
  • MSC (2000): Primary 13P10
  • DOI:
  • MathSciNet review: 2470810