An extension of Wif's conjecture to affine semigroups

Abstract

Let C ⊂ Q_+^p 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 the C-semigroups with minimal embedding dimension.We extendWilf’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.