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The asymptotic distribution of leaf heights in binary trees

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Abstract

Let ℬ n be the family of extended binary tress withn internal nodes and assume that eacht ∈ℬ n has equal probability. We identify the asymptotic distribution of the height of leafi (where the leaves are enumerated from left to right) asi andn tend to infinity, such thati/n tends tox λ]0, 1[, as a Maxwell distribution. A generalization of the used combinatorial resp. probabilistic considerations is indicated.

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Authors and Affiliations

  1. Department of Statistics, Applied Mathematics and Computation, University of Vienna, Universitaetsstrasse 5-9, A-1010, Wien, Austria

    W. Gutjahr & G. C. Pflug

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  1. W. Gutjahr
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  2. G. C. Pflug
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Gutjahr, W., Pflug, G.C. The asymptotic distribution of leaf heights in binary trees. Graphs and Combinatorics 8, 243–251 (1992). https://doi.org/10.1007/BF02349961

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  • DOI: https://doi.org/10.1007/BF02349961

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