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Postorder trees and Eulerian numbers

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Abstract

Binary search trees built from the postorder traversal sequence of other binary search trees are characterized in terms of their binary tree structure. A connection is established between this structure and the Eulerian numbers. This yields considerable information concerning the “average” binary search tree with a given number of nodes. Periodicity is established for the process of repeatedly taking postorder sequences and building binary search trees. Finally, the average depth of a node in a postorder tree withn nodes is determined.

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Authors and Affiliations

  1. Department of Computer Science, Washington and Lee University, 24450, Lexington, VA, USA

    Thomas P. Whaley

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  1. Thomas P. Whaley
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Whaley, T.P. Postorder trees and Eulerian numbers. Acta Informatica 28, 703–712 (1991). https://doi.org/10.1007/BF01178684

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  • DOI: https://doi.org/10.1007/BF01178684

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