Protected points in ordered trees

doi:10.1016/j.aml.2007.07.001

Applied Mathematics Letters

Volume 21, Issue 5, May 2008, Pages 516-520

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Abstract

In this note we start by computing the average number of protected points in all ordered trees with $n$ edges. This can serve as a guide in various organizational schemes where it may be desirable to have a large or small number of protected points. We will also look a few subclasses with a view to increasing or decreasing the proportion of protected points.

Keywords

Ordered tree

Protected point

Catalan number

Fine number

Central binomial coefficient

Motzkin numbers

{0, 1, 2}

-trees