Random Monomial Ideals
Commutative Algebra
2018-01-08 v2 Combinatorics
Probability
Abstract
Inspired by the study of random graphs and simplicial complexes, and motivated by the need to understand average behavior of ideals, we propose and study probabilistic models of random monomial ideals. We prove theorems about the probability distributions, expectations and thresholds for events involving monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers, and present several experimentally-backed conjectures about regularity, projective dimension, strong genericity, and Cohen-Macaulayness of random monomial ideals.
Cite
@article{arxiv.1701.07130,
title = {Random Monomial Ideals},
author = {Jesus A. De Loera and Sonja Petrovic and Lily Silverstein and Despina Stasi and Dane Wilburne},
journal= {arXiv preprint arXiv:1701.07130},
year = {2018}
}
Comments
26 pages, 8 figures. This version fixes a few of typographical errors, shortens and improves section 2.1