Binomial fibers and indispensable binomials

Abstract

Let $I$ be an arbitrary ideal generated by binomials. We show that certain equivalence classes of fibers are associated to any minimal binomial generating set of $I$. We provide a simple and efficient algorithm to compute the indispensable binomials of a binomial ideal from a given generating set of binomials and an algorithm to detect whether a binomial ideal is generated by indispensable binomials.

15 pages, 2 figures. All results have been extended to the general case of binomial ideals. Several proofs were added/modified and there is a new theorem, Theorem 1.8. The paper will appear in Journal of Symbolic Computation

References in corpus (2)

• Indispensable monomials of toric ideals and Markov bases
• Graver Bases and Universal Gröbner Bases for Linear Codes