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.
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- Hidefumi Ohsugi
- Affiliation: Department of Mathematics, College of Science, Rikkyo University, Toshima, Tokyo 171-8501, Japan
- Email: firstname.lastname@example.org
- 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: email@example.com
- 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: https://doi.org/10.1090/S0002-9939-08-09675-5
- MathSciNet review: 2470810