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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 2, Pages 384–392 (Mi smj2204)  

This article is cited in 1 scientific paper (total in 1 paper)

Clique matchings in the $k$-ary $n$-dimensional cube

V. N. Potapovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk, Russia
Full-text PDF (328 kB) Citations (1)
References:
Abstract: A clique matching in the $k$-ary $n$-dimensional cube (hypercube) is a collection of disjoint one-dimensional faces. A clique matching is called perfect if it covers all vertices of the hypercube. We show that the number of perfect clique matchings in the $k$-ary $n$-dimensional cube can be expressed as the $k$-dimensional permanent of the adjacency array of some hypergraph. We calculate the order of the logarithm of the number of perfect clique matchings in the $k$-ary $n$-dimensional cube for an arbitrary positive integer $k$ as $n\to\infty$.
A perfect clique matching is called precise if each two-dimensional face of the hypercube includes a sole one-dimensional face of the clique matching. Precise clique matchings are particular cases of H-designs. We prove that for the existence of precise clique matchings in the $k$-ary $n$-dimensional cube it is necessary that $k=2m$ and $n=4m$ for some positive integer m. We propose a construction of precise clique matchings for $k=2^t$ and $n=2^{t+1}$ with an arbitrary positive integer $t$.
Keywords: perfect matching, clique matching, permanent, MDS code, H-design.
Received: 07.04.2010
Revised: 24.12.2010
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 2, Pages 303–310
DOI: https://doi.org/10.1134/S0037446611020133
Bibliographic databases:
Document Type: Article
UDC: 519.14
Language: Russian
Citation: V. N. Potapov, “Clique matchings in the $k$-ary $n$-dimensional cube”, Sibirsk. Mat. Zh., 52:2 (2011), 384–392; Siberian Math. J., 52:2 (2011), 303–310
Citation in format AMSBIB
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\by V.~N.~Potapov
\paper Clique matchings in the $k$-ary $n$-dimensional cube
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 2
\pages 384--392
\mathnet{http://mi.mathnet.ru/smj2204}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2841556}
\transl
\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 2
\pages 303--310
\crossref{https://doi.org/10.1134/S0037446611020133}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955768217}
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  • https://www.mathnet.ru/eng/smj/v52/i2/p384
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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