Apéry sets of shifted numerical monoids

Abstract

A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid $S$, consider the family of "shifted" monoids $M_n$ obtained by adding $n$ to each generator of $S$. In this paper, we characterize the Apéry set of $M_n$ in terms of the Apéry set of the base monoid $S$ when $n$ is sufficiently large. We give a highly efficient algorithm for computing the Apéry set of $M_n$ in this case, and prove that several numerical monoid invariants, such as the genus and Frobenius number, are eventually quasipolynomial as a function of $n$.

References in corpus (3)

• On the set of elasticities in numerical monoids
• Numerical semigroups on compound sequences
• Factorization invariants in numerical monoids

Cited by in corpus (5)

• Canonical trace ideal and residue for numerical semigroup rings
• Betti numbers for numerical semigroup rings
• Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups
• On Frobenius Numbers of Shifted Power Sequences
• On minimal presentations of shifted affine semigroups with few generators