Characterization of perfect numerical semigroups in terms of pseudo-Frobenius numbers

Abstract

In the theory of numerical semigroups, characterizing numerical semigroups in terms of pseudo-Frobenius numbers is one of the fundamental problems, which is very difficult to achieve in general. This article's main purpose is to answer this problem in the case of perfect numerical semigroups having a Maximal Embedding Dimension (MED).

Keywords

• Numerical semigroup
• Isolated gap
• Pseudo-Frobenius