On coincidences of tuples in a binary tree with random labels of vertices
-
Andrey M. Zubkov
and
Vasiliy I. Kruglov
Abstract
Let all vertices of a complete binary tree of finite height be independently and equiprobably labeled by the elements of some finite alphabet. We consider the numbers of pairs of identical tuples of labels on chains of subsequent vertices in the tree. Exact formulae for the expectations of these numbers are obtained. Convergence to the compound Poisson distribution is proved.
Funding: This work was supported by the Russian Science Foundation under grant no. 14-50-00005.
Originally published in Diskretnaya Matematika (2015) 27, No4, 3-20 (in Russian).
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