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Protected points in ordered trees

โœ Scribed by Gi-Sang Cheon; Louis W. Shapiro

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
198 KB
Volume
21
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

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.

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Let Qn.k,, be the number of all n-node ordered trees with r nodes of maximum level k and let B,,\*,, be the number of all r-tuply rooted ordered trees with n nodes and height less than or equal to k. In this paper we derive the identitity where n, k, r > 0. An explicit expression for Qn,k,r and its