Algorithms and basic asymptotics for generalized numerical semigroups in \(\mathbb N^d\)

DOI10.1007/s00233-015-9690-8zbMath1384.20047OpenAlexW1996138197WikidataQ60691918 ScholiaQ60691918MaRDI QIDQ283342

Chris Peterson, Rosanna Utano, Gioia Failla

Publication date: 13 May 2016

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

Full work available at URL: https://doi.org/10.1007/s00233-015-9690-8

zbMATH Keywords

monoidnumerical semigroupFrobenius number

Mathematics Subject Classification ID

Nonnumerical algorithms (68W05) Commutative semigroups (20M14) Software, source code, etc. for problems pertaining to group theory (20-04) Semigroups (20M99)

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Uses Software

• NumericalSemigroupsWithGenus
• OEIS

Cites Work

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• Constructing the set of complete intersection numerical semigroups with a given Frobenius number.
• Counting numerical semigroups by genus and some cases of a question of Wilf.
• On the enumeration of the set of numerical semigroups with fixed Frobenius number.
• The Frobenius problem for numerical semigroups
• On the variety of linear recurrences and numerical semigroups
• Improved bounds on the number of numerical semigroups of a given genus
• Constructing numerical semigroups of a given genus.
• Bounds on the number of numerical semigroups of a given genus
• Numerical semigroups.
• On finitely generated submonoids of \(\mathbb{N}^ k\)
• Genus of numerical semigroups generated by three elements.
• \(\mathbb N\)-solutions to linear systems over \(\mathbb Z\)
• The set of numerical semigroups of a given genus.
• Fibonacci-like growth of numerical semigroups of a given genus.
• Fibonacci-like behavior of the number of numerical semigroups of a given genus.
• Towards a better understanding of the semigroup tree
• Two-Generator Numerical Semigroups and Fermat and Mersenne Numbers
• COUNTING NUMERICAL SEMIGROUPS WITH SHORT GENERATING FUNCTIONS
• A Circle-Of-Lights Algorithm for the "Money-Changing Problem"
• PRESENTATIONS OF FINITELY GENERATED SUBMONOIDS OF FINITELY GENERATED COMMUTATIVE MONOIDS
• On numerical semigroups