An extension of Wilf's conjecture to affine semigroups

DOI10.1007/s00233-017-9906-1zbMath1456.20065arXiv1608.08528OpenAlexW2963823500WikidataQ122982396 ScholiaQ122982396MaRDI QIDQ1644740

Alberto Vigneron-Tenorio, Juan Ignacio García García, Daniel Marín Aragon

Publication date: 22 June 2018

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

Full work available at URL: https://arxiv.org/abs/1608.08528

zbMATH Keywords

genusembedding dimensionFrobenius numberaffine semigroupWilf's conjecturesemigroup tree

Mathematics Subject Classification ID

Commutative semigroups (20M14) Other combinatorial number theory (11B75) Arithmetic theory of semigroups (20M13)

Related Items

The corner element of generalized numerical semigroups ⋮ Characterizing affine \(\mathcal{C}\)-semigroups ⋮ Quasi-polynomial growth of numerical and affine semigroups with constrained gaps ⋮ A characterization of some families of Cohen-Macaulay, Gorenstein and/or Buchsbaum rings ⋮ A geometrical characterization of proportionally modular affine semigroups ⋮ Affine semigroups of maximal projective dimension ⋮ Some properties of affine \({\mathcal{C}}\)-semigroups ⋮ On generalized Wilf conjectures ⋮ A generalization of Wilf's conjecture for generalized numerical semigroups ⋮ Affine semigroups of maximal projective dimension. II ⋮ On divisor-closed submonoids and minimal distances in finitely generated monoids ⋮ Type and conductor of simplicial affine semigroups ⋮ Algorithms for generalized numerical semigroups ⋮ On pseudo-Frobenius elements of submonoids of \(\mathbb{N}^d\) ⋮ On almost-symmetry in generalized numerical semigroups ⋮ On numerical semigroups with at most 12 left elements

Uses Software

• Mathematica
• Normaliz
• LattE
• Python

Cites Work

• Algorithms and basic asymptotics for generalized numerical semigroups in \(\mathbb N^d\)
• Counting numerical semigroups by genus and some cases of a question of Wilf.
• Numerical semigroups.
• Fibonacci-like growth of numerical semigroups of a given genus.
• On a conjecture by Wilf about the Frobenius number
• Fibonacci-like behavior of the number of numerical semigroups of a given genus.
• Exploring the tree of numerical semigroups
• A Circle-Of-Lights Algorithm for the "Money-Changing Problem"
• Ideals, Varieties, and Algorithms