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
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
- 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, DOI 10.1007/978-1-4757-2181-2
- H. Hara, A. Takemura and R. Yoshida, Markov bases for two-way subtable sum problems, arXiv:math.CO/0708.2312v1, 2007.
- Hidefumi Ohsugi and Takayuki Hibi, Toric ideals generated by quadratic binomials, J. Algebra 218 (1999), no. 2, 509–527. MR 1705794, DOI 10.1006/jabr.1999.7918
- 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
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
- MR Author ID: 219759
- Email: hibi@math.sci.osaka-u.ac.jp
- 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