Abstract:   The main concern of this paper is with a bijective approach to various classes of increasing trees. We discover an increasing tree counterpart of the decomposition algorithm for Schröder trees. This bijection has probably reached its full generality for decomposing increasing trees. As a special case of our algorithm, we provide a solution to a problem concerning the enumeration of plane trees by the net number of inversions.

  Keywords:  increasing trees, Schröder trees, bijections.