# Almost symmetric numerical semigroups with high type

## TL;DR

This paper explores the relationship between numerical semigroups and almost symmetric numerical semigroups, establishing a precise correspondence under certain conditions related to genus and Frobenius number.

## Contribution

It introduces a one-to-one correspondence between numerical semigroups of a given genus and almost symmetric semigroups with specific Frobenius number and type, under a new condition.

## Key findings

- Established a bijection between numerical semigroups and almost symmetric semigroups.
- Identified conditions relating Frobenius number, type, and genus.
- Extended understanding of the structure of numerical semigroups.

## Abstract

We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater than $4g-1$.