An Algebra for Proper Generating Trees

We nd an algebraic structure for a subclass of generating trees by introducing the concept of marked generating trees. In these kind of trees, labels can be marked or non marked and the count relative to a certain label at a certain level is given by the diierence between the number of non marked and marked labels. The algebraic structure corresponds to a non commu-tative group with respect to a product operation between two generating trees. Hence we deene the identity generating tree and the inverse of a given generating tree.