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.
CITATION STYLE
Hackl, B., Heuberger, C., Kropf, S., & Prodinger, H. (2018). Fringe analysis of plane trees related to cutting and pruning. Aequationes Mathematicae, 92(2), 311–353. https://doi.org/10.1007/s00010-017-0529-0
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