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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
DOI: https://doi.org/10.1090/S0002-9939-08-09675-5
Published electronically: December 5, 2008
MathSciNet review: 2470810
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Abstract | References | Similar Articles | Additional Information

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?)

  • 1. David Cox, John Little, and Donal O’Shea, Ideals, varieties, and algorithms, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1992. An introduction to computational algebraic geometry and commutative algebra. MR 1189133
  • 2. H. Hara, A. Takemura and R. Yoshida, Markov bases for two-way subtable sum problems, arXiv:math.CO/0708.2312v1, 2007.
  • 3. Hidefumi Ohsugi and Takayuki Hibi, Toric ideals generated by quadratic binomials, J. Algebra 218 (1999), no. 2, 509–527. MR 1705794, https://doi.org/10.1006/jabr.1999.7918
  • 4. 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.
  • 5. Bernd Sturmfels, Gröbner bases and convex polytopes, University Lecture Series, vol. 8, American Mathematical Society, Providence, RI, 1996. MR 1363949

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Additional Information

Hidefumi Ohsugi
Affiliation: Department of Mathematics, College of Science, Rikkyo University, Toshima, Tokyo 171-8501, Japan
Email: ohsugi@rkmath.rikkyo.ac.jp

Takayuki Hibi
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: hibi@math.sci.osaka-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-08-09675-5
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.