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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2019 Volume 482, Pages 244–258 (Mi znsl6840)

$\pm1$-matrices with vanishing permanent

K. A. Taranin

Lomonosov Moscow State University

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.

UDC: 512.643, 512.643.2

Received: 07.10.2019



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