An extension of Wilf’s conjecture to affine semigroups

Let C ⊂ Q + p be a rational cone. An affine semigroup S ⊂ C is a C -semigroup whenever ( C \ S ) ∩ N p has only a finite number of elements. In this work, we study the tree of C -semigroups, give a method to generate it and study the C -semigroups with minimal embedding dimension. We extend Wilf’s c...

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Bibliographic Details
Published in:Semigroup forum 2018-04, Vol.96 (2), p.396-408
Main Authors: García-García, J. I., Marín-Aragón, D., Vigneron-Tenorio, A.
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Research Article
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Summary:Let C ⊂ Q + p be a rational cone. An affine semigroup S ⊂ C is a C -semigroup whenever ( C \ S ) ∩ N p has only a finite number of elements. In this work, we study the tree of C -semigroups, give a method to generate it and study the C -semigroups with minimal embedding dimension. We extend Wilf’s conjecture for numerical semigroups to C -semigroups and give some families of C -semigroups fulfilling the extended conjecture. Other conjectures formulated for numerical semigroups are also studied for C -semigroups.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-017-9906-1