Ordinarization of Numerical Semigroups

This procedure allows the construction of a tree for each given genus containing all semigrpoups of that genus and rooted in the unique ordinary semigroup of that genus. We study here the regularity of these trees and the number of semigroups at each depth. For some depths it is proved that the number of semigroups increases with the genus and it is conjectured that this happens at all given depths. This may give some lights to a former conjecture saying that the number of semigroups of a given genus increases with the genus.