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Aequationes mathematicae

, Volume 92, Issue 2, pp 311–353 | Cite as

Fringe analysis of plane trees related to cutting and pruning

  • Benjamin Hackl
  • Clemens Heuberger
  • Sara Kropf
  • Helmut Prodinger
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 

Notes

Acknowledgements

Open access funding provided by University of Klagenfurt

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institut für MathematikAlpen-Adria-Universität KlagenfurtKlagenfurtAustria
  2. 2.Institute of Statistical ScienceAcademia SinicaTaipeiTaiwan
  3. 3.Department of Mathematical SciencesStellenbosch UniversityStellenboschSouth Africa

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