English

Numerical Semigroups Generated by Quadratic Sequences

Group Theory 2020-09-07 v1

Abstract

We investigate numerical semigroups generated by any quadratic sequence with initial term zero and an infinite number of terms. We find an efficient algorithm for calculating the Ap\'ery set, as well as bounds on the elements of the Ap\'ery set. We also find bounds on the Frobenius number and genus, and the asymptotic behavior of the Frobenius number and genus. Finally, we find the embedding dimension of all such numerical semigroups.

Keywords

Cite

@article{arxiv.2009.01981,
  title  = {Numerical Semigroups Generated by Quadratic Sequences},
  author = {Mara Hashuga and Megan Herbine and Alathea Jensen},
  journal= {arXiv preprint arXiv:2009.01981},
  year   = {2020}
}

Comments

37 pages

R2 v1 2026-06-23T18:18:31.133Z