Random numerical semigroups and a simplicial complex of irreducible semigroups
Commutative Algebra
2017-10-25 v2 Combinatorics
Abstract
We examine properties of random numerical semigroups under a probabilistic model inspired by the Erdos-Renyi model for random graphs. We provide a threshold function for cofiniteness, and bound the expected embedding dimension, genus, and Frobenius number of random semigroups. Our results follow, surprisingly, from the construction of a very natural shellable simplicial complex whose facets are in bijection with irreducible numerical semigroups of a fixed Frobenius number and whose -vector determines the probability that a particular element lies in the semigroup.
Cite
@article{arxiv.1710.00979,
title = {Random numerical semigroups and a simplicial complex of irreducible semigroups},
author = {Jesus De Loera and Christopher O'Neill and Dane Wilburne},
journal= {arXiv preprint arXiv:1710.00979},
year = {2017}
}