Modularly equidistant numerical semigroups

Authors

JOSÉ CARLOS ROSALES
MANUEL BAPTISTA BRANCO
MÁRCIO ANDRE TRAESEL

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.

DOI

10.3906/mat-2008-83

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