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Diskretnaya Matematika, 2018, Volume 30, Issue 3, Pages 48–67
DOI: https://doi.org/10.4213/dm1537 (Mi dm1537) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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
Full-text PDF (540 kB) Citations (3)
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DOI: https://doi.org/10.4213/dm1537
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
Received: 08.03.2018
English version:
Discrete Mathematics and Applications, 2018, Volume 28, Issue 5, Pages 293–307
DOI: https://doi.org/10.1515/dma-2018-0026
Bibliographic databases:
Document Type: Article
UDC: 519.212.2
Language: Russian
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
Citation in format AMSBIB
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\jour Discrete Math. Appl.
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретная математика
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