English

Factorization length distribution for affine semigroups I: numerical semigroups with three generators

Commutative Algebra 2021-02-05 v2 Combinatorics

Abstract

Most factorization invariants in the literature extract extremal factorization behavior, such as the maximum and minimum factorization lengths. Invariants of intermediate size, such as the mean, median, and mode factorization lengths are more subtle. We use techniques from analysis and probability to describe the asymptotic behavior of these invariants. Surprisingly, the asymptotic median factorization length is described by a number that is usually irrational.

Keywords

Cite

@article{arxiv.1804.05135,
  title  = {Factorization length distribution for affine semigroups I: numerical semigroups with three generators},
  author = {Stephan Ramon Garcia and Christopher O'Neill and Samuel Yih},
  journal= {arXiv preprint arXiv:1804.05135},
  year   = {2021}
}

Comments

17 pages

R2 v1 2026-06-23T01:23:27.059Z