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

## TL;DR

This paper solves a fundamental problem in numerical semigroup theory by characterizing perfect semigroups with maximal embedding dimension using pseudo-Frobenius numbers.

## Contribution

The paper provides a characterization of perfect numerical semigroups with maximal embedding dimension using pseudo-Frobenius numbers.

## Key findings

- Perfect numerical semigroups with maximal embedding dimension can be characterized using pseudo-Frobenius numbers.
- The characterization addresses a fundamental problem in numerical semigroup theory.
- The approach is specific to perfect semigroups with maximal embedding dimension.

## 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).