On Some Numerical Semigroup Transforms

In this paper we introduce a particular semigroup transform $\mathcal{A}$ that fixes the invariants involved in Wilf's conjecture, except embedding dimension. It also allows one to arrange set of not ordinary and irreducible numerical semigroups family rooted trees. We study another transform, having similar features, has been introduced by Bras-Amor\'os, make comparison them. behaviour dimension under action such transforms, providing some consequences concerning conjecture.