Quasi-ordinarization transform of a numerical semigroup

Abstract

We present the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups of that genus. This construction provides an alternative approach to the conjecture on the increasingness of the number of numerical semigroups of each given genus. We elaborate on the number of nodes at each tree depth in the forest and present new conjectures.