Small Groebner Fans of Ideals of Points
Commutative Algebra
2024-11-19 v2
Abstract
In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Groebner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this property. Moreover, we provide methodologies for constructing such ideals. We then relax the condition of uniqueness. The second and most relevant topic discussed here is to consider and identify pairs of ideals with the same number of reduced Groebner bases, that is, with the same cardinality of their associated Groebner fan.
Keywords
Cite
@article{arxiv.1704.03680,
title = {Small Groebner Fans of Ideals of Points},
author = {Elena Dimitrova and Qijun He and Lorenzo Robbiano and Brandilyn Stigler},
journal= {arXiv preprint arXiv:1704.03680},
year = {2024}
}
Comments
Many improvements. Accepted for publication in Journal of Algebra and its Applications