V. Ponomarenko

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math.AC2025

On numerical semigroup elements and the $ℓ_{0}$ - and $ℓ_{\infty}$ -norms of their factorizations

Sogol Cyrusian, Alex Domat, Christopher O'Neill +3

A numerical semigroup $S$ is a cofinite, additively-closed subset of $Z_{\geq 0}$ that contains 0, and a factorization of $x \in S$ is a $k$ -tuple $z = (z_{1}, \dots, z_{k})$ w…

math.AC2025

Betti elements and full atomic support in rings and monoids

Scott T. Chapman, Pedro García-Sánchez, Christopher O'Neill +1

Several papers in the recent literature have studied factorization properties of affine monoids using the monoid's Betti elements. In this paper, we extend this study to more gener…

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.AC2024

Perspicacious $l_{p}$ norm parameters

Christopher O'Neill, Vadim Ponomarenko, Eric Ren

Fix $t \in [1, \infty]$ . Let $S$ be an atomic commutative semigroup and, for all $x \in S$ , let $L_{t} (S) := {∥ f ∥_{t} : f \in Z (x)}$ be the " $t$ -length set" of $x$ (using the sta…

On numerical semigroup elements and the ℓ0​- and ℓ∞​-norms of their factorizations

Betti elements and full atomic support in rings and monoids

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

Perspicacious lp​ norm parameters

On numerical semigroup elements and the $ℓ_{0}$ - and $ℓ_{\infty}$ -norms of their factorizations

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

Perspicacious $l_{p}$ norm parameters