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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 958–965
(Mi semr540)
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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
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
Citation:
A. A. Taranenko, “Upper bounds on the permanent of multidimensional $(0,1)$-matrices”, Sib. Èlektron. Mat. Izv., 11 (2014), 958–965
Linking options:
https://www.mathnet.ru/eng/semr540 https://www.mathnet.ru/eng/semr/v11/p958
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Abstract page: | 179 | Full-text PDF : | 67 | References: | 34 |
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