Constructing numerical semigroups of a given genus.

DOI10.1007/s00233-009-9190-9zbMath1204.20080arXiv0910.2075OpenAlexW2073841927WikidataQ60691917 ScholiaQ60691917MaRDI QIDQ972584

Yufei Zhao

Publication date: 21 May 2010

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.2075

zbMATH Keywords

Fibonacci numbersgenusnumerical semigroupsasymptotic boundsnumbers of semigroups

Mathematics Subject Classification ID

Commutative semigroups (20M14) Asymptotic results on counting functions for algebraic and topological structures (11N45) Asymptotic enumeration (05A16)

Related Items (27)

Frobenius R-variety of the numerical semigroups contained in a given one ⋮ Algorithms and basic asymptotics for generalized numerical semigroups in \(\mathbb N^d\) ⋮ The proportion of Weierstrass semigroups ⋮ Distribution of genus among numerical semigroups with fixed Frobenius number ⋮ Counting Numerical Semigroups ⋮ Quasi-polynomial growth of numerical and affine semigroups with constrained gaps ⋮ The set of numerical semigroups of a given genus. ⋮ The ordinarization transform of a numerical semigroup and semigroups with a large number of intervals. ⋮ Counting the ideals with given genus of a numerical semigroup ⋮ Sub-Fibonacci behavior in numerical semigroup enumeration ⋮ Conjecture of Wilf: A Survey ⋮ Gapsets of Small Multiplicity ⋮ Counting numerical semigroups by genus and some cases of a question of Wilf. ⋮ Sets characterized by missing sums and differences ⋮ Fibonacci-like growth of numerical semigroups of a given genus. ⋮ Elasticity in Apéry Sets ⋮ Degree asymptotics of the numerical semigroup tree. ⋮ Unnamed Item ⋮ Computation of numerical semigroups by means of seeds ⋮ Subsemigroup, ideal and congruence growth of free semigroups ⋮ The set of numerical semigroups of a given multiplicity and Frobenius number ⋮ Unnamed Item ⋮ Gapsets and numerical semigroups ⋮ Almost-positioned numerical semigroups ⋮ Numerical semigroups with concentration two ⋮ Positioned numerical semigroups ⋮ COUNTING NUMERICAL SEMIGROUPS WITH SHORT GENERATING FUNCTIONS

Uses Software

• OEIS

Cites Work

• Improved bounds on the number of numerical semigroups of a given genus
• Bounds on the number of numerical semigroups of a given genus
• Representation of numerical semigroups by Dyck paths.
• Fibonacci-like behavior of the number of numerical semigroups of a given genus.
• Towards a better understanding of the semigroup tree

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