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Two way subtable sum problems and quadratic Gröbner bases

Authors: Hidefumi Ohsugi and Takayuki Hibi
Journal: Proc. Amer. Math. Soc. 137 (2009), 1539-1542
MSC (2000): Primary 13P10
Published electronically: December 5, 2008
MathSciNet review: 2470810
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Abstract: 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.

References [Enhancements On Off] (What's this?)

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Additional Information

Hidefumi Ohsugi
Affiliation: Department of Mathematics, College of Science, Rikkyo University, Toshima, Tokyo 171-8501, Japan

Takayuki Hibi
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan

Keywords: Quadratic Gr\"obner bases, toric ideals
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.