For two decades, the Colless index has been the most frequently used statistic for assessing
the balance of phylogenetic trees. In this article, this statistic is studied under the Yule and …

A heap ordered tree with $ n $ nodes (" size $ n $") is a planted plane tree together with a
bijection from the nodes to the set $\{1,\dots, n\} $ which is monotonically increasing when …

A fine analysis is given of the transitional behavior of the average cost of quicksort with
median-of-three. Asymptotic formulae are derived for the stepwise improvement of the …

This paper presents an analytic approach to the construction cost of fringe-balanced binary
search trees. In [7], Mahmoud used a bottom-up approach and an urn model of Pólya. The …

Hoare's Find algorithm can be used to select p specified order statistics j1,…, jp from a file of
n elements simultaneously. Averaging over all np subsets of 1,…, n defines the grand …

In [1] the concept of nondecreasing Dyck paths was introduced. We continue this research
by looking at it from the point of view of words, rational languages, planted plane trees, and …

There are three classical algorithms to visit all the nodes of a binary tree-preorder, inorder
and postorder traversal. From this one gets a natural labelling of the n internal nodes of a …

We investigate incomplete one-sided variants of binary search trees. The (normed) size of
each variant is studied, and convergence to a Gaussian law is proved in each case by …

In this work we introduce randomized insertion and deletion algorithms for quad trees.
These algorithms are simple and they are defined for any dimension K (where K is a natural …

The Number of Descendants in Simply Generated Random Trees 1 Introduction Page 1 Trends in
Mathematics, © 2000 Birkhiiuser Verlag Basel/Switzerland The Number of Descendants in Simply …