# Fibonacci-Like Behavior of the Number of Numerical Semigroups of a Given Genus

## TL;DR

This paper explores a Fibonacci-like pattern in the count of numerical semigroups for each genus and hypothesizes that the related sequence converges to the golden ratio, supported by computational evidence up to genus 50.

## Contribution

It introduces a novel Fibonacci-like conjecture on numerical semigroup counts and their asymptotic behavior, supported by computational data.

## Key findings

- Number of numerical semigroups of a given genus exhibits Fibonacci-like growth.
- The quotient sequence of these counts appears to approach the golden ratio.
- The Wilf conjecture has been verified for all semigroups with genus up to 50.

## Abstract

We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the number of semigroups of genus at most 50. The Wilf conjecture has also been checked for all numerical semigroups with genus in the same range.