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Aequationes mathematicae

, Volume 90, Issue 3, pp 625–645 | Cite as

The height of multiple edge plane trees

  • Clemens Heuberger
  • Helmut Prodinger
  • Stephan Wagner
Open Access
Article

Abstract

Multi-edge trees as introduced in a recent paper of Dziemiańczuk are plane trees where multiple edges are allowed. We first show that d-ary multi-edge trees where the out-degrees are bounded by d are in bijection with classical d-ary trees. This allows us to analyse parameters such as the height. The main part of this paper is concerned with multi-edge trees counted by their number of edges. The distribution of the number of vertices as well as the height are analysed asymptotically.

Keywords

Multi-edge tree Plane tree d-ary tree Height Limit distributions 

Mathematics Subject Classification

05A16 05A15 05C05 60C05 

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Copyright information

© The Author(s) 2015

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.Department of Mathematical SciencesStellenbosch UniversityStellenboschSouth Africa

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