Enumeration of Matchings in Complete -ary Trees

We study the asymptotic behavior of the parameters and , that equal the number of matchings and independent matchings in a complete -ary tree of height . We show that, for any , there exists a such that, as , the following asymptotic equality holds: We also show that, for any , there exist numbers a...

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Bibliographic Details
Published inMathematical Notes Vol. 111; no. 3-4; pp. 398 - 406
Main Authors Kuz’min, N. A., Malyshev, D. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2022
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Asymptotic properties
Enumeration
Mathematics
Mathematics and Statistics
ary tree
independent matching
complete
limit theorem
matching
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Summary:We study the asymptotic behavior of the parameters and , that equal the number of matchings and independent matchings in a complete -ary tree of height . We show that, for any , there exists a such that, as , the following asymptotic equality holds: We also show that, for any , there exist numbers and such that as , and also, for any sufficiently large , there exist numbers and such that, as , the following asymptotic equalities hold:
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434622030075