Reflective numerical semigroups
Number Theory
2022-07-04 v1
Abstract
We define a reflective numerical semigroup of genus as a numerical semigroup that has a certain reflective symmetry when viewed within as an array with columns. Equivalently, a reflective numerical semigroup has one gap in each residue class modulo . In this paper, we give an explicit description for all reflective numerical semigroups. With this, we can describe the reflective members of well-known families of numerical semigroups as well as obtain formulas for the number of reflective numerical semigroups of a given genus or given Frobenius number.
Cite
@article{arxiv.2207.00051,
title = {Reflective numerical semigroups},
author = {Caleb M. Shor},
journal= {arXiv preprint arXiv:2207.00051},
year = {2022}
}