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Two way subtable sum problems and quadratic Gröbner bases
Author(s):
Hidefumi
Ohsugi;
Takayuki
Hibi
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1539-1542.
MSC (2000):
Primary 13P10
Posted:
December 5, 2008
MathSciNet review:
2470810
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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:
-
- 1.
- D. Cox, J. Little and D. O'Shea, Ideals, Varieties and Algorithms, Springer-Verlag, Berlin-Heidelberg-New York, 1992. MR 1189133 (93j:13031)
- 2.
- H. Hara, A. Takemura and R. Yoshida, Markov bases for two-way subtable sum problems, arXiv:math.CO/0708.2312v1, 2007.
- 3.
- H. Ohsugi and T. Hibi, Toric ideals generated by quadratic binomials, J. Algebra 218 (1999), 509-527. MR 1705794 (2000f:13055)
- 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.
- B. Sturmfels, Gröbner Bases and Convex Polytopes, Amer. Math. Soc., Providence, RI, 1996. MR 1363949 (97b:13034)
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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:
10.1090/S0002-9939-08-09675-5
PII:
S 0002-9939(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
Posted:
December 5, 2008
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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