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

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.

Keywords:

• Factorization
• mean
• median
• mode
• monoid
• numerical semigroup
• quasipolynomial
• quasirational function

2020 Mathematics Subject Classification:

• 20M14
• 05E40

Additional information

Funding

This work was partially supported by NSF grants DMS-1800123 and DMS-2054002.