The problem of finding (−1, 1)-matrices with vanishing permanent was posed 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 ≤ 5. Bibliography: 20 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 482, 2019, pp. 244–258.
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Taranin, K.A. ±1-Matrices with Vanishing Permanent. J Math Sci 249, 271–280 (2020). https://doi.org/10.1007/s10958-020-04941-8
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DOI: https://doi.org/10.1007/s10958-020-04941-8