COUNTING NUMERICAL SEMIGROUPS WITH SHORT GENERATING FUNCTIONS

DOI10.1142/S0218196711006911zbMath1250.20048arXiv0901.1228WikidataQ58217183 ScholiaQ58217183MaRDI QIDQ3112587

Víctor Blanco, Pedro A. García Sánchez, Justo Puerto

Publication date: 11 January 2012

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.1228

zbMATH Keywords

generating functionsmultiplicitiesnumerical semigroupsgeneraFrobenius numberscounting algorithms

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Commutative semigroups (20M14) Counting solutions of Diophantine equations (11D45) Lattice points in specified regions (11P21)

Related Items (17)

Algorithms and basic asymptotics for generalized numerical semigroups in \(\mathbb N^d\) ⋮ Counting numerical semigroups by genus and even gaps ⋮ Presburger Arithmetic, Rational Generating Functions, and Quasi-Polynomials ⋮ Counting Numerical Semigroups ⋮ Irreducible numerical semigroups with multiplicity three and four. ⋮ 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. ⋮ Parametrizing Arf numerical semigroups ⋮ Counting numerical semigroups by genus and some cases of a question of Wilf. ⋮ Parametrizing numerical semigroups with multiplicity up to 5 ⋮ 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 ⋮ An improved algorithm to compute the \(\omega\)-primality ⋮ Square-free divisor complexes of certain numerical semigroup elements

Uses Software

• numericalsgps
• NumericalSemigroupsWithGenus

Cites Work

• Unnamed Item
• The Frobenius problem for numerical semigroups
• Parametric integer programming algorithm for bilevel mixed integer programs
• Numerical semigroups with multiplicity three and four.
• Improved bounds on the number of numerical semigroups of a given genus
• Constructing numerical semigroups of a given genus.
• Counting integer points in parametric polytopes using Barvinok's rational functions
• Bounds on the number of numerical semigroups of a given genus
• Numerical semigroups.
• Non-Weierstrass numerical semigroups
• Fundamental gaps in numerical semigroups.
• Counting with rational generating functions
• Fibonacci-like behavior of the number of numerical semigroups of a given genus.
• Short rational functions for toric algebra and applications
• Towards a better understanding of the semigroup tree
• SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS
• Short rational generating functions for lattice point problems
• A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed
• On Counting Integral Points in a Convex Rational Polytope

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