Iterative Cutting of Non-Catalan Trees
VeranstaltungsortI.0.07Veranstalter Institut für MathematikBeschreibungIn previous work, several deterministic reduction procedures on plane trees (e.g. cutting away all leaves or cutting away all maximal paths ending in a leaf) have been studied. In this context, a parameter of particular interest is the number of removed nodes after iteratively applying the reduction a fixed number of times to a given plane tree.After briefly revisiting the previous results, we will discuss a new modeling approach based on a recursive description using additive tree parameters. Effectively, this new strategy leads to functional equations for the appropriate bivariate generating functions and thus allows us to analyze the behavior of a deterministic reduction acting on tree classes that are not part of the Catalan family. In the scope of this talk we will focus on the "cutting leaves"-reduction applied to the class of simply generated trees (i.e., a generalization of plane trees) and the class of Pólya trees (unordered, rooted trees).Vortragende(r)Benjamin HacklKontaktSenka Haznadar (senka.omerhodzic@aau.at)
