Constructing numerical semigroups of a given genus
By Yufei Zhao. 2009
46 citations recorded by the source corpus.
Let ng denote the number of numerical semigroups of genus g. Bras-Amorós conjectured that ng 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 ng.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/53dd19fac45652ce2e84c9abcbc597229afb1998
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Sets characterized by missing sums and differences (2009, methodology): “The techniques used in this paper have also inspired a new approach to a different problem on counting numerical semigroups of a given genus [15].”
- Counting numerical semigroups by genus and some cases of a question of Wilf (2012, result): “We also discuss connections with recent work of Blanco, Garćıa-Sánchez and Puerto, and mention several further open problems.”
- Fibonacci-like growth of numerical semigroups of a given genus (2011, background): “Zhao showed in [8] that it is at least 3.”