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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 482, Pages 244–258 (Mi znsl6840)  

$\pm1$-matrices with vanishing permanent

K. A. Taranin

Lomonosov Moscow State University
References:
Abstract: The problem of finding $(-1,1)$-matrices with permanent $0$ was proposed by Edward Wang in 1974. This paper states and proves bounds on the number of negative entries in a matrix with zero permanent and minimal number of negative entries among all matrices of the same equivalence class. Then representatives of every equivalence class of matrices with zero permanent are found for $n\leq 5$.
Key words and phrases: permanent, $\pm1$-matrices, vanishing.
Funding agency Grant number
Russian Science Foundation 17-11-01124
Received: 07.10.2019
Document Type: Article
UDC: 512.643, 512.643.2
Language: Russian
Citation: K. A. Taranin, “$\pm1$-matrices with vanishing permanent”, Computational methods and algorithms. Part XXXII, Zap. Nauchn. Sem. POMI, 482, POMI, St. Petersburg, 2019, 244–258
Citation in format AMSBIB
\Bibitem{Tar19}
\by K.~A.~Taranin
\paper $\pm1$-matrices with vanishing permanent
\inbook Computational methods and algorithms. Part~XXXII
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 482
\pages 244--258
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6840}
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  • https://www.mathnet.ru/eng/znsl/v482/p244
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