English

On the Linearity of \omega-primality in Numerical Monoids

Commutative Algebra 2018-08-15 v3 Combinatorics

Abstract

In an atomic, cancellative, commutative monoid, the \omega-value measures how far an element is from being prime. In numerical monoids, we show that this invariant exhibits eventual quasilinearity (i.e., periodic linearity). We apply this result to describe the asymptotic behavior of the \omega-function for a general numerical monoid and give an explicit formula when the monoid has embedding dimension 2.

Keywords

Cite

@article{arxiv.1309.7476,
  title  = {On the Linearity of \omega-primality in Numerical Monoids},
  author = {Christopher O'Neill and Roberto Pelayo},
  journal= {arXiv preprint arXiv:1309.7476},
  year   = {2018}
}