Numerical Semigroups with $a_e = 2g+1$
Group Theory
2026-04-27 v1 Commutative Algebra
Number Theory
Abstract
This article discusses numerical semigroups having a generator which is as large as possible. This turns out to be , where is the genus of the semigroup. We will show that these semigroups are closely related to symmetric semigroups and have interesting symmetry properties themselves. Furthermore we will show that Wilf's question has a positive answer for these semigroups and some semigroups derived thereof.
Cite
@article{arxiv.2604.21948,
title = {Numerical Semigroups with $a_e = 2g+1$},
author = {Michael Hellus and Reinhold Hübl and Anton Rechenauer},
journal= {arXiv preprint arXiv:2604.21948},
year = {2026}
}