On numerical semigroups closed with respect to the action of affine maps

TL;DR

This paper investigates numerical semigroups that are closed under affine maps, providing formulas and methods to determine their minimal generators, embedding dimension, genus, and Frobenius number.

Contribution

It introduces a systematic study of numerical semigroups closed under affine maps and derives key invariants for these semigroups.

Findings

Derived minimal generating sets for these semigroups

Computed their embedding dimension, genus, and Frobenius number

Provided structural insights into semigroups with affine closure

Abstract

In this paper we study numerical semigroups containing a given positive integer and closed with respect to the action of an affine map. For such semigroups we find a minimal set of generators, their embedding dimension, their genus and their Frobenius number.