Aequationes mathematicae

, Volume 92, Issue 2, pp 311–353

# Fringe analysis of plane trees related to cutting and pruning

Open Access
Article

## Abstract

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.

## Keywords

Plane trees Pruning Tree reductions Central limit theorem Narayana polynomials

## Mathematics Subject Classification

05A16 05C05 05A15 05A19 60C05

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