34 citations · 239 across the 41 of their papers we have counts for
10 papers · 1 filter
On arithmetical numerical monoids with some generators omitted
Sung Hyup Lee, Christopher O'Neill, Brandon Van Over
Numerical monoids (cofinite, additive submonoids of the non-negative integers) arise frequently in additive combinatorics, and have recently been studied in the context of factoriz…
Random numerical semigroups and a simplicial complex of irreducible semigroups
Jesus De Loera, Christopher O'Neill, Dane Wilburne
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 cofinitene…
On mesoprimary decomposition of monoid congruences
Christopher O'Neill
We prove two main results concerning mesoprimary decomposition of monoid congruences, as introduced by Kahle and Miller. First, we identify which associated prime congruences appea…
Apéry sets of shifted numerical monoids
Christopher O'Neill, Roberto Pelayo
A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid , consider the family of "shifted" monoids obtained by adding to eac…
A computer algebra system for R: Macaulay2 and the m2r package
David Kahle, Christopher O'Neill, Jeff Sommars
Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings…
Some algebraic aspects of mesoprimary decomposition
Laura Felicia Matusevich, Christopher O'Neill
Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing "mesoprimary decompositions" determined by their un…
Realizable sets of catenary degrees of numerical monoids
Christopher O'Neill, Roberto Pelayo
The catenary degree is an invariant that measures the distance between factorizations of elements within an atomic monoid. In this paper, we classify which finite subsets of $\math…
Unimodular hierarchical models and their Graver bases
Daniel Irving Bernstein, Christopher O'Neill
Given a simplicial complex whose vertices are labeled with positive integers, one can associate a vector configuration whose corresponding toric variety is the Zariski closure of a…
The Elasticity of Puiseux Monoids
Felix Gotti, Christopher O'Neill
Let be an atomic monoid and let be a non-unit element of . The elasticity of , denoted by , is the ratio of its largest factorization length to its shortest fac…
Minimal presentations of shifted numerical monoids
Rebecca Conaway, Felix Gotti, Jesse Horton +4
A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid , consider the family of "shifted" monoids obtained by adding to eac…