NUMERICAL SEMIGROUPS WITH MONOTONIC AP´ERY SET

Abstract

We study numerical semigroups S with the property that if m is the multiplicity of S and w(i) is the least element of S congruent with i modulo m, then 0 < w(1) < : : : < w(m 􀀀 1). The set of numerical semigroups with this property and xed multiplicity is bijective with an a ne semigroup and consequently it can be described by a nite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.