English

A sequence of quasipolynomials arising from random numerical semigroups

Combinatorics 2018-09-27 v1 Commutative Algebra

Abstract

A numerical semigroup is a subset of the non-negative integers that is closed under addition. For a randomly generated numerical semigroup, the expected number of minimum generators can be expressed in terms of a doubly-indexed sequence of integers, denoted hn,ih_{n, i}, that count generating sets with certain properties. We prove a recurrence that implies the sequence hn,ih_{n,i} is eventually quasipolynomial when the second parameter is fixed.

Keywords

Cite

@article{arxiv.1809.09915,
  title  = {A sequence of quasipolynomials arising from random numerical semigroups},
  author = {Calvin Leng and Christopher O'Neill},
  journal= {arXiv preprint arXiv:1809.09915},
  year   = {2018}
}
R2 v1 2026-06-23T04:18:51.305Z