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math.AC2022
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…
math.AC2022
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 …
math.AC2022
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…