Modularly equidistant numerical semigroups

Abstract

If S is a numerical semigroup and s ∈ S , we denote by nextS(s) = min {x ∈ S | s < x}. Let a be an integer greater than or equal to two. A numerical semigroup is equidistant modulo a if nextS(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.