34 citations · 239 across the 41 of their papers we have counts for
28 papers · 1 filter
Numerical semigroups via projections and via quotients
Tristram Bogart, Christopher O'Neill, Kevin Woods
We examine two natural operations to create numerical semigroups. We say that a numerical semigroup is -normalescent if it is the projection of the set of integer…
When is a numerical semigroup a quotient?
Tristram Bogart, Christopher O'Neill, Kevin Woods
A natural operation on numerical semigroups is taking a quotient by a positive integer. If is a quotient of a numerical semigroup with generators, we call $\mathca…
Graver bases of shifted numerical semigroups with 3 generators
James Howard, Christopher O'Neill
A numerical semigroup is a subset of the non-negative integers that is closed under addition. A factorization of is an expression of as a sum of generators of …
Convexity in (colored) affine semigroups
Jesus A. De Loera, Christopher O'Neill, Chengyang Wang
In this paper, we explore affine semigroup versions of the convex geometry theorems of Helly, Tverberg, and Caratheodory. Additionally, we develop a new theory of colored affine se…
Length density and numerical semigroups
Cole Brower, Scott Chapman, Travis Kulhanek +4
Length density is a recently introduced factorization invariant, assigned to each element of a cancellative commutative atomic semigroup , that measures how far the set of f…
On length densities
Scott T. Chapman, Christopher O'Neill, Vadim Ponomarenko
For a commutative cancellative monoid , we introduce the notion of the length density of both a nonunit , denoted , and the entire monoid , denoted $\…
On parametrized families of numerical semigroups
Franklin Kerstetter, Christopher O'Neill
A numerical semigroup is an additive subsemigroup of the non-negative integers. In this paper, we consider parametrized families of numerical semigroups of the form $P_n = \langle…
Elasticity in Apery sets
Jackson Autry, Tara Gomes, Christopher O'Neill +1
A numerical semigroup is an additive subsemigroup of the non-negative integers, containing zero, with finite complement. Its multiplicity is its smallest nonzero element. T…
Beyond Coins, Stamps, and Chicken McNuggets: an Invitation to Numerical Semigroups
Scott Chapman, Rebecca Garcia, Christopher O'Neill
We give a self contained introduction to numerical semigroups, and present several open problems centered on their factorization properties.
Augmented Hilbert series of numerical semigroups
Jeske Glenn, Christopher O'Neill, Vadim Ponomarenko +1
A numerical semigroup is a subset of the non-negative integers containing that is closed under addition. The Hilbert series of (a formal power series equal to the sum o…
Squarefree divisor complexes of certain numerical semigroup elements
Jackson Autry, Paige Graves, Jessie Loucks +3
A numerical semigroup is an additive subsemigroup of the non-negative integers with finite complement, and the squarefree divisor complex of an element is a simplicia…
Factorization length distribution for affine semigroups I: numerical semigroups with three generators
Stephan Ramon Garcia, Christopher O'Neill, Samuel Yih
Most factorization invariants in the literature extract extremal factorization behavior, such as the maximum and minimum factorization lengths. Invariants of intermediate size, suc…
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…
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…
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…
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…
Mesoprimary decomposition of binomial submodules
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…
Factorization invariants in numerical monoids
Christopher O'Neill, Roberto Pelayo
Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization struc…
On dynamic algorithms for factorization invariants in numerical monoids
Thomas Barron, Christopher O'Neill, Roberto Pelayo
Studying the factorization theory of numerical monoids relies on understanding several important factorization invariants, including length sets, delta sets, and -primality. Whi…
On the set of catenary degrees of finitely generated cancellative commutative monoids
Christopher O'Neill, Vadim Ponomarenko, Reuben Tate +1
The catenary degree of an element of a cancellative commutative monoid is a nonnegative integer measuring the distance between the irreducible factorizations of . The ca…
On factorization invariants and Hilbert functions
Christopher O'Neill
Nonunique factorization in cancellative commutative semigroups is often studied using combinatorial factorization invariants, which assign to each semigroup element a quantity dete…