Minimal systems of binomial generators and the indispensable complex of a toric ideal

Authors:
Hara Charalambous, Anargyros Katsabekis and Apostolos Thoma

Journal:
Proc. Amer. Math. Soc. **135** (2007), 3443-3451

MSC (2000):
Primary 13F20, 05C99

DOI:
https://doi.org/10.1090/S0002-9939-07-09037-5

Published electronically:
July 3, 2007

MathSciNet review:
2336556

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a vector configuration and its corresponding toric ideal. The paper consists of two parts. In the first part we completely determine the number of different minimal systems of binomial generators of . In the second part we associate to a simplicial complex . We show that the vertices of correspond to the indispensable monomials of the toric ideal , while one dimensional facets of with minimal binomial -degree correspond to the indispensable binomials of .

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Additional Information

**Hara Charalambous**

Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

Email:
hara@math.auth.gr

**Anargyros Katsabekis**

Affiliation:
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece

Email:
akatsabekis@in.gr

**Apostolos Thoma**

Affiliation:
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece

Email:
athoma@cc.uoi.gr

DOI:
https://doi.org/10.1090/S0002-9939-07-09037-5

Keywords:
Toric ideal,
minimal systems of generators,
indispensable monomials,
indispensable binomials

Received by editor(s):
July 10, 2006

Published electronically:
July 3, 2007

Additional Notes:
This research was co-funded by the European Union in the framework of the program “Pythagoras" of the “Operational Program for Education and Initial Vocational Training" of the 3rd Community Support Framework of the Hellenic Ministry of Education.

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.