Factorization length distribution for affine semigroups III: modular equidistribution for numerical semigroups with arbitrarily many generators

TL;DR

This paper investigates the distribution of factorization lengths in numerical semigroups with multiple generators, demonstrating their equidistribution across various modular classes under broad conditions.

Contribution

It establishes the asymptotic equidistribution of factorization lengths in numerical semigroups with arbitrary generators across different modular classes.

Findings

Factorization lengths are equidistributed across non-trivial modular classes.

The distribution holds asymptotically for numerical semigroups with many generators.

The results extend understanding of factorization behavior in complex semigroups.

Abstract

For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrary modulus. In particular, we prove that the factorization lengths are equidistributed across all congruence classes that are not trivially ruled out by modular considerations.