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Mat. Vopr. Kriptogr., 2019, Volume 10, Issue 4, Pages 9–24 (Mi mvk305)  

Asymptotic properties of the inversion number in colored trees

V. A. Vatutin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We consider a $b$-ary plane rooted tree $T$ whose vertices are colored independently and equiprobably in $m$ colors labelled with letters of an alphabet $\mathcal{A}=\{ A_{1}<A_{2}<...<A_{m}\} .$ A vertex $u\in T$ is an ancestor of a vertex $v\in T$ ($u\prec v),$ if the path leading along the edges from the root of the tree to the vertex $v$ passes through the vertex $u$. Denote $col(u)$ the color of the vertex $u.$ The coloring of the pair $u\prec v$ forms an inversion if $col(u)>col(v).$ We study the probabilistic characteristics of the total number of inversions in a colored $b$-ary plane rooted tree of a fixed height and the distribution of random variables that are functionals of the number of inversions in the subtrees of such a tree.

Key words: $b$-ary plane rooted tree, colored tree, inversion, limit theorems.

DOI: https://doi.org/10.4213/mvk305

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Bibliographic databases:

UDC: 519.212.2+519.214
Received 29.IV.2019

Citation: V. A. Vatutin, “Asymptotic properties of the inversion number in colored trees”, Mat. Vopr. Kriptogr., 10:4 (2019), 9–24

Citation in format AMSBIB
\Bibitem{Vat19}
\by V.~A.~Vatutin
\paper Asymptotic properties of the inversion number in colored trees
\jour Mat. Vopr. Kriptogr.
\yr 2019
\vol 10
\issue 4
\pages 9--24
\mathnet{http://mi.mathnet.ru/mvk305}
\crossref{https://doi.org/10.4213/mvk305}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3869632}


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