Christopher O’Neill

collaborators

3 papers

math.AC2024

Some asymptotic results on $p$ -lengths of factorizations for numerical semigroups and arithmetical congruence monoids

Spencer Chapman, Eli B. Dugan, Shadi Gaskari +4

A factorization of an element $x$ in a monoid $(M, \cdot)$ is an expression of the form $x = u_{1}^{z_{1}} \dots u_{k}^{z_{k}}$ for irreducible elements $u_{1}, \dots, u_{k} \in M$ , and the…

math.CO2024

Numerical semigroups from rational matrices II: matricial dimension does not exceed multiplicity

Arsh Chhabra, Stephan Ramon Garcia, Christopher O'Neill

We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least g…

math.NT2023

Atomic density of arithmetical congruence monoids

Nils Olsson, Christopher O'Neill, Derek Rawling

Consider the set $M_{a, b} = {n \in Z_{\geq 1} : n \equiv a mod b} \cup {1}$ for $a, b \in Z_{\geq 1}$ . If $a^{2} \equiv a mod b$ , then $M_{a, b}$ is closed under…

Some asymptotic results on p-lengths of factorizations for numerical semigroups and arithmetical congruence monoids

Numerical semigroups from rational matrices II: matricial dimension does not exceed multiplicity

Atomic density of arithmetical congruence monoids

Some asymptotic results on $p$ -lengths of factorizations for numerical semigroups and arithmetical congruence monoids