Linear non-homogenous patterns and prime power generators in numerical semigroups associated to combinatorial configurations

TL;DR

This paper investigates the structure of numerical semigroups linked to combinatorial configurations, demonstrating they satisfy specific non-linear symmetric patterns and analyzing particular classes of these configurations.

Contribution

It introduces the existence of non-linear symmetric patterns in numerical semigroups associated with combinatorial configurations and studies their properties in specific cases.

Findings

Numerical semigroups satisfy non-linear symmetric patterns.

Analysis of semigroups for particular combinatorial configurations.

Identification of prime power generators within these semigroups.

Abstract

It is proved that the numerical semigroups associated to the combinatorial configurations satisfy a family of non-linear symmetric patterns. Also, these numerical semigroups are studied for two particular classes of combinatorial configurations.