Factorization length distribution for affine semigroups IV: a geometric approach to weighted factorization lengths in three-generator numerical semigroups

TL;DR

This paper investigates the asymptotic distribution of weighted factorization lengths in three-generator numerical semigroups, offering a geometric approach that generalizes prior results with explicit error bounds.

Contribution

It introduces a geometric method to analyze weighted factorization lengths, extending previous work and providing clearer proofs and explicit error estimates.

Findings

Asymptotic behavior characterized for weighted factorization lengths

Explicit error bounds derived for the distribution

Generalization of previous results to a geometric framework

Abstract

For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals of the coefficients in the factorizations of semigroup elements. This work generalizes many previous results, provides more natural and intuitive proofs, and yields a completely explicit error bound.