An extension of Wilf's conjecture to affine semigroups

Abstract

Let C ⊂ Qp be a rational cone. An affine semigroup S ⊂ C is a C-semigroup whenever (C \ S) ∩ Np 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 their subsemigroups 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. We also check that other conjectures on numerical semigroups seem to be also satisfied by C-semigroups.