An extension of Wilf's conjecture to affine semigroups

作者：Garcia-Garcia J. I.^*; Marin-Aragon D.; Vigneron-Tenorio A.

来源：Semigroup Forum, 2018, 96(2): 396-408.

DOI：10.1007/s00233-017-9906-1

• Affine semigroup
• Embedding dimension
• Frobenius number
• Genus
• Semigroup tree
• Wilf's conjecture

Let be a rational cone. An affine semigroup is a -semigroup whenever has only a finite number of elements. In this work, we study the tree of -semigroups, give a method to generate it and study the -semigroups with minimal embedding dimension. We extend Wilf's conjecture for numerical semigroups to -semigroups and give some families of -semigroups fulfilling the extended conjecture. Other conjectures formulated for numerical semigroups are also studied for -semigroups.

• 出版日期2018-4