Growing and Destroying Classes of Plane Trees

Motivated by an interpretation of the well-known register function on binary trees as the age of the tree with respect to a particular growth process, we investigated similar growth procedures and their reduction counterparts on plane trees. For some rather straightforward growth procedures, parameters like the age and the growth over some number of generations could be proven to exhibit a similar asymptotic behavior. 

In this talk, we study a growth process generating a large subclass of plane trees, for which a fundamentally different asymptotic behavior manifests in the parameters of interest.