Constructing Numerical Semigroups of a Given Genus
Combinatorics
2015-10-26 v1 Commutative Algebra
Abstract
Let n_g denote the number of numerical semigroups of genus g. Bras-Amoros conjectured that n_g possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree. We offer a new, simpler approach to counting numerical semigroups of a given genus. Our method gives direct constructions of families of numerical semigroups, without referring to the generators or the semigroup tree. In particular, we give an improved asymptotic lower bound for n_g.
Cite
@article{arxiv.0910.2075,
title = {Constructing Numerical Semigroups of a Given Genus},
author = {Yufei Zhao},
journal= {arXiv preprint arXiv:0910.2075},
year = {2015}
}
Comments
11 pages, 3 figures, 2 tables; accepted by Semigroup Forum