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.
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