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 , that count generating sets with certain properties. We prove a recurrence that implies the sequence is eventually quasipolynomial when the second parameter is fixed.
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}
}