Counting vertices in labeled rooted trees

Series
Combinatorics Seminar
Time
Friday, April 21, 2017 - 3:05pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Miklós Bóna – University of Florida – bona@ufl.eduhttp://people.clas.ufl.edu/bona/
Organizer
Torin Greenwood
Various parameters of many models of random rooted trees are fairly well understood if they relate to a near-root part of the tree or to global tree structure. In recent years there has been a growing interest in the analysis of the random tree fringe, that is, the part of the tree that is close to the leaves. Distance from the closest leaf can be viewed as the protection level of a vertex, or the seniority of a vertex within a network. In this talk we will review a few recent results of this kind for a number of tree varieties, as well as indicate the challenges one encounters when trying to generalize the existing results. One tree variety, that of decreasing binary trees, will be related to permutations, another one, phylogenetic trees, is frequent in applications in molecular biology.