|
Indispensable binomials in semigroup ideals
Author(s):
Ignacio
Ojeda;
Alberto
Vigneron-Tenorio
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4205-4216.
MSC (2010):
Primary 13F20;
Secondary 16W50, 13F55
Posted:
June 30, 2010
MathSciNet review:
2680047
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, we deal with the problem of the uniqueness of a minimal system of binomial generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient conditions for the uniqueness of such a minimal system of generators. These conditions come from the study and combinatorial description of the so-called indispensable binomials in the semigroup ideal.
References:
-
- 1.
- S. Aoki, A. Takemura, R. Yoshida,
Indispensable monomials of toric ideals and Markov bases, J. Symbolic Comput. 43 (2008), no. 6-7, 490-507. MR 2406969 (2009c:13065) - 2.
- A. Bigatti, R. La Scala, L. Robbiano,
Computing toric ideals,
J. Symbolic Comput. 27 (1999), 351-365. MR 1681344 (2000b:13035) - 3.
- E. Briales, A. Campillo, C. Marijuán, P. Pisón,
Combinatorics of syzygies for semigroup algebra,
Collect. Math. 49 (1998), 239-256. MR 1677160 (99m:13024) - 4.
- E. Briales, A. Campillo, C. Marijuán, P. Pisón,
Minimal systems of generators for ideals of semigroups,
J. Pure Appl. Algebra, 124 (1998), 7-30. MR 1600261 (98k:20105) - 5.
- H. Charalambous, A. Katsabekis, A. Thoma,
Minimal systems of binomial generators and the indispensable complex of a toric ideal,
Proc. Amer. Math. Soc. 135 (2007), 3443-3451. MR 2336556 (2009a:13033) - 6.
- H. Charalambous, A. Thoma,
On simple  -multigraded minimal resolutions,
Contemporary Mathematics, Vol. 502, Amer. Math. Soc., 2009, pp. 33-44. - 7.
- P. Diaconis, B. Sturmfels,
Algebraic algorithms for sampling from conditional distributions,
Ann. Statist. 26(1) (1998), 363-397. MR 1608156 (99j:62137) - 8.
- D. Eisenbud, B. Sturmfels,
Binomial ideals,
Duke Math. J. 84 (1996), no. 1, 1-45. MR 1394747 (97d:13031) - 9.
- S. Eliahou,
Courbes monomiales et algébre de Rees symbolique,
PhD Thesis, Université of Genève, 1983. - 10.
- D. Geiger, C. Meek, B. Sturmfels,
On the toric algebra of graphical models,
Ann. Statist. 34 (2006), no. 3, 1463-1492. MR 2278364 (2007m:60035) - 11.
- J. Herzog,
Generators and relations of abelian semigroups and semigroup rings,
Manuscripta Math. 3 (1970), 175-193. MR 0269762 (42:4657) - 12.
- E. Miller, B. Sturmfels,
Combinatorial Commutative Algebra.
Vol. 227 of Graduate Texts in Mathematics. Springer, New York, 2005. MR 2110098 (2006d:13001) - 13.
- H. Ohsugi, T. Hibi,
Indispensable binomials of finite graphs,
J. Algebra Appl. 4 (2005), no. 4, 421-434. MR 2166253 (2006e:13023) - 14.
- H. Ohsugi, 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. MR 2394671 (2009c:13070) - 15.
- I. Ojeda, A. Vigneron-Tenorio,
Simplicial complexes and minimal free resolution of monomial algebras.
J. Pure Appl. Algebra 214 (2010), no. 6, 850-861. - 16.
- I. Ojeda, P. Pisón-Casares,
On the hull resolution of an affine monomial curve,
J. Pure Appl. Algebra 192 (2004), 53-67. MR 2067188 (2005e:13018) - 17.
- I. Ojeda,
Examples of generic lattice ideals of codimension 3,
Comm. Algebra 36 (2008), 279-287. MR 2381125 (2008j:13027) - 18.
- I. Peeva, B. Sturmfels,
Generic lattice ideals,
J. Amer. Math. Soc. 11 (1998), 363-373. MR 1475887 (98i:13022) - 19.
- I. Peeva, B. Sturmfels,
Syzygies of codimension  lattice ideals,
Math. Z. 229 (1998), 163-194. MR 1649322 (99g:13020) - 20.
- P. Pisón-Casares, A. Vigneron-Tenorio,
On Lawrence semigroups,
J. Symbolic Comput. 43 (2008), 804-810. MR 2432958 (2009i:20128) - 21.
- J.C. Rosales, P.A. García-Sánchez,
Finitely generated commutative monoids,
Nova Science Publishers, Inc., New York, 1999. MR 1694173 (2000d:20074) - 22.
- B. Sturmfels,
Gröbner bases and convex polytopes,
volume 8 of University Lecture Series,
American Mathematical Society, Providence, RI, 1996. MR 1363949 (97b:13034) - 23.
- A. Takemura, S. Aoki,
Some characterizations of minimal Markov basis for sampling from discrete conditional distributions,
Ann. Inst. Statist. Math. 56(1) (2004), 1-17. MR 2053726 (2005g:62103)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2010):
13F20,
16W50, 13F55
Retrieve articles in all Journals with
MSC (2010):
13F20,
16W50, 13F55
Additional Information:
Ignacio
Ojeda
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, E-06071 Badajoz, Spain
Email:
ojedamc@unex.es
Alberto
Vigneron-Tenorio
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, E-11405 Jerez de la Frontera, Spain
Email:
alberto.vigneron@uca.es
DOI:
10.1090/S0002-9939-2010-10456-2
PII:
S 0002-9939(2010)10456-2
Keywords:
Semigroup ideal,
indispensable binomial,
minimal system of generators,
Markov basis,
simplicial complex,
toric ideal,
monomial algebra
Received by editor(s):
October 23, 2009
Received by editor(s) in revised form:
February 22, 2010
Posted:
June 30, 2010
Additional Notes:
Both authors are partially supported by the project MTM2007-64704, National Plan I+D+I. The first author is partially supported by Junta de Extremadura (ayuda a grupos GRU09104) and FEDER funds
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
