Benjamin Hackl, Clemens Heuberger, Sara Kropf, Helmut Prodinger
Published 2017-04-04Version 1
Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations include cutting all or only the leftmost leaves or maximal paths. This generalizes the concept of pruning a tree. The results include exact expressions and asymptotic expansions for the expected value and the variance as well as central limit theorems.
The Hypercube of Resistors, Asymptotic Expansions, and Preferential Arrangements
Central Limit Theorems for some Set Partition Statistics
De Moivre and Bell polynomials
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