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November 2001 The Profile of Binary Search Trees
Brigitte Chauvin, Michael Drmota, Jean Jabbour-Hattab
Ann. Appl. Probab. 11(4): 1042-1062 (November 2001). DOI: 10.1214/aoap/1015345394

Abstract

We characterize the limiting behavior of the number of nodes in level $k$ of binary search trees $T_n$ in the central region $1.2 \log n \leq 2.8 \log n$. Especially we show that the width $\bar{V}_n$ (the maximal number of internal nodes at the same level) satisfies $\bar{V}_n \sim (n/\sqrt{4\pi\log n})$ as $n \to \infty$ a.s.

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Brigitte Chauvin. Michael Drmota. Jean Jabbour-Hattab. "The Profile of Binary Search Trees." Ann. Appl. Probab. 11 (4) 1042 - 1062, November 2001. https://doi.org/10.1214/aoap/1015345394

Information

Published: November 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1012.60038
MathSciNet: MR1878289
Digital Object Identifier: 10.1214/aoap/1015345394

Subjects:
Primary: 05C05 , 60F17 , 60Q25

Keywords: asymptotic series expansion , complex analysis , Martingales , Repartition of nodes for binary search trees

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.11 • No. 4 • November 2001
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