34 citations · 239 across the 41 of their papers we have counts for
5 papers · 1 filter
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…
Enumerating numerical sets associated to a numerical semigroup
April Chen, Nathan Kaplan, Liam Lawson +2
A numerical set is a subset of that contains and has finite complement. The atom monoid of is the set of such that .…
On the cardinality of minimal presentations of numerical semigroups
Ceyhun Elmacioglu, Kieran Hilmer, Christopher O'Neill +2
In this paper, we consider the following question: "given the multiplicity and embedding dimension of a numerical semigroup , what can be said about the cardinality …