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Diskretnyi Analiz i Issledovanie Operatsii, 2016, Volume 23, Issue 4, Pages 35–101
DOI: https://doi.org/10.17377/daio.2016.23.517 (Mi da858) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Permanents of multidimensional matrices: properties and applications

A. A. Taranenko

Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
Full-text PDF (507 kB) Citations (14)
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DOI: https://doi.org/10.17377/daio.2016.23.517
Abstract: The permanent of a multidimensional matrix is the sum of the products of entries over all diagonals. In this survey, we consider the basic properties of the multidimensional permanent, sufficient conditions for its positivity, available upper bounds, and the specifics of the permanents of polystochastic matrices. We prove that the number of various combinatorial objects can be expressed via multidimensional permanents. Special attention is paid to the number of $1$-factors of uniform hypergraphs and the number of transversals in Latin hypercubes. Tabl. 1, bibliogr. 63.
Keywords: permanent, multidimensional matrix, stochastic matrix, polystochastic matrix, transversal in a Latin hypercube, $1$-factor of a uniform hypergraph.
Funding agency Grant number
Russian Science Foundation 14-11-00555
Möbius Contest
Received: 13.11.2015
English version:
Journal of Applied and Industrial Mathematics, 2016, Volume 10, Issue 4, Pages 567–604
DOI: https://doi.org/10.1134/S1990478916040141
Bibliographic databases:
Document Type: Article
UDC: 519.1
Language: Russian
Citation: A. A. Taranenko, “Permanents of multidimensional matrices: properties and applications”, Diskretn. Anal. Issled. Oper., 23:4 (2016), 35–101; J. Appl. Industr. Math., 10:4 (2016), 567–604
Citation in format AMSBIB
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\by A.~A.~Taranenko
\paper Permanents of multidimensional matrices: properties and applications
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 4
\pages 35--101
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\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 4
\pages 567--604
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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