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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Number 4, Pages 35–101 (Mi da858)  

This article is cited in 4 scientific papers (total in 4 papers)

Permanents of multidimensional matrices: properties and applications

A. A. Taranenko

Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

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


DOI: https://doi.org/10.17377/daio.2016.23.517

Full text: PDF file (507 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:4, 567–604

Bibliographic databases:

UDC: 519.1
Received: 13.11.2015

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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\paper Permanents of multidimensional matrices: properties and applications
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\pages 35--101
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\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
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\crossref{https://doi.org/10.1134/S1990478916040141}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Taranenko, “On the Number of Transversals in $n$-Ary Quasigroups of Order 4”, Math. Notes, 101:5 (2017), 919–921  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Q.-W. Wang, F. Zhang, “The permanent functions of tensors”, Acta Math. Vietnam, 43:4, SI (2018), 701–713  crossref  mathscinet  zmath  isi  scopus
    3. A. Taranenko, “Transversals, plexes, and multiplexes in iterated quasigroups”, Electron. J. Comb., 25:4 (2018), P4.30  mathscinet  zmath  isi
    4. E. G. Belei, A. A. Semenov, “O sposobakh propozitsionalnogo kodirovaniya razlichimosti ob'ektov v konechnykh mnozhestvakh”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 28 (2019), 3–20  mathnet  crossref
  • Дискретный анализ и исследование операций
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