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Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 451–456 (Mi semr500)  

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

Discrete mathematics and mathematical cybernetics

On the multidimensional permanent and $q$-ary designs

V. N. Potapovab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia

Abstract: An $H(n,q,w,t)$ design is a collection of some $(n-w)$-faces of the hypercube $Q^n_q$ that perfectly pierce all $(n-t)$-faces $(n\geq w>t)$. An $A(n,q,w,t)$ design is a collection of some $(n-t)$-faces of $Q^n_q$ that perfectly cover all $(n-w)$-faces. The numbers of H-designs and A-designs are expressed in terms of the multidimensional permanent. Several constructions of H-designs and A-designs are given and the existence of $H(2^{t+1},s2^t,2^{t+1}-1,2^{t+1}-2)$ designs is proven for all $s,t\geq 1$.

Keywords: Steiner system, H-design, perfect matching, clique matching, MDS code, permanent.

Full text: PDF file (520 kB)
References: PDF file   HTML file
UDC: 519.14
MSC: 05B05, 05C65
Received April 6, 2014, published June 16, 2014

Citation: V. N. Potapov, “On the multidimensional permanent and $q$-ary designs”, Sib. Èlektron. Mat. Izv., 11 (2014), 451–456

Citation in format AMSBIB
\Bibitem{Pot14}
\by V.~N.~Potapov
\paper On the multidimensional permanent and $q$-ary designs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 451--456
\mathnet{http://mi.mathnet.ru/semr500}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Taranenko, “Permanents of multidimensional matrices: properties and applications”, J. Appl. Industr. Math., 10:4 (2016), 567–604  mathnet  crossref  crossref  mathscinet  elib
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