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Diskr. Mat., 2018, Volume 30, Issue 3, Pages 48–67 (Mi dm1537)  

On coincidences of tuples in a $q$-ary tree with random labels of vertices

V. I. Kruglov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Let all vertices of a complete $q$-ary 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. For the size of cluster composed by pairs of identically labeled chains we also obtain exact formula for the expectation.

Keywords: $q$-ary trees with random labels, matches of labels, sums of dependent indicators, Poisson approximation

Funding Agency Grant Number
Russian Science Foundation 14-50-00005


DOI: https://doi.org/10.4213/dm1537

Full text: PDF file (540 kB)
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English version:
Discrete Mathematics and Applications, 2018, 28:5, 293–307

Bibliographic databases:

Document Type: Article
UDC: 519.212.2
Received: 08.03.2018

Citation: V. I. Kruglov, “On coincidences of tuples in a $q$-ary tree with random labels of vertices”, Diskr. Mat., 30:3 (2018), 48–67; Discrete Math. Appl., 28:5 (2018), 293–307

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  • Дискретная математика
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