Binomial fibers and indispensable binomials

TL;DR

This paper introduces algorithms to identify indispensable binomials in binomial ideals and explores the relationship between fibers and minimal generating sets, enhancing understanding of binomial ideal structure.

Contribution

It presents new algorithms for detecting indispensable binomials and links fibers to minimal generating sets in binomial ideals.

Findings

Algorithms for computing indispensable binomials

Method to determine if an ideal is generated by indispensable binomials

Connection between fibers and minimal binomial generating sets

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.