Modularly equidistant numerical semigroups

Authors

JOSÉ CARLOS ROSALES
MANUEL BAPTISTA BRANCO
MÁRCIO ANDRE TRAESEL

DOI

10.3906/mat-2008-83

Abstract

IfS is a numerical semigroup and s ∈ S , we denote by next$_{S}$(s) = min {x ∈ S s < x}. Leta be an integer greater than or equal to two. A numerical semigroup is equidistant modulo a if next$_{S}$((s) - s - 1 is a multiple of a for every s ∈ S . In this note, we give algorithms for computing the whole set of equidistant numerical semigroups modulo a with fixed multiplicity, genus, and Frobenius number. Moreover, we will study this kind of semigroups with maximal embedding dimension.

Keywords

Embedding dimension, Frobenius number, genus, multiplicity, modularly equidistant numerical semigroups, MED semigroups, numerical semigroup

First Page

288

Last Page

299

Recommended Citation

ROSALES, JOSÉ CARLOS; BRANCO, MANUEL BAPTISTA; and TRAESEL, MÁRCIO ANDRE (2021) "Modularly equidistant numerical semigroups," Turkish Journal of Mathematics: Vol. 45: No. 1, Article 17. https://doi.org/10.3906/mat-2008-83
Available at: https://journals.tubitak.gov.tr/math/vol45/iss1/17