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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 958–965 (Mi semr540)  
This article is cited in 2 scientific papers (total in 2 papers)

Discrete mathematics and mathematical cybernetics

Upper bounds on the permanent of multidimensional $(0,1)$-matrices

A. A. Taranenkoab

a Novosibirsk State University, Pirogova, 2, 630090, Novosibirsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
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Abstract: The permanent of a multidimensional matrix is the sum of products of entries over all diagonals.
By Minc's conjecture, there exists a reachable upper bound on the permanent of $2$-dimensional $(0,1)$-matrices. In this paper we obtain some generalizations of Minc's conjecture to the multidimensional case. For this purpose we prove and compare several bounds on the permanent of multidimensional $(0,1)$-matrices.
Most estimates can be used for matrices with nonnegative bounded entries.
Keywords: permanent, multidimensional matrix, $(0,1)$-matrix.
Received October 31, 2014, published December 8, 2014
Document Type: Article
UDC: 519.143.3
MSC: 05A20
Language: English
Citation: A. A. Taranenko, “Upper bounds on the permanent of multidimensional $(0,1)$-matrices”, Sib. Èlektron. Mat. Izv., 11 (2014), 958–965
Citation in format AMSBIB
\Bibitem{Tar14}
\by A.~A.~Taranenko
\paper Upper bounds on the permanent of multidimensional $(0,1)$-matrices
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 958--965
\mathnet{http://mi.mathnet.ru/semr540}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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