Iterative Cutting of Non-Catalan Trees
Veranstaltungsort
I.0.07
Veranstalter
Institut für Mathematik
Beschreibung
In 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 Hackl
Kontakt
Senka Haznadar (senka [dot] omerhodzic [at] aau [dot] at)
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