Abstract
Let Ω n denote the set of alln×n (1, − 1)-matrices. In 1974 E. T. H. Wang posed the following problems: Is there a decent upper bound for |perA| whenAσΩ n is nonsingular? We recently conjectured that the best possible bound is the permanent of the matrix with exactlyn−1 negative entries in the main diagonal, and affirmed that conjecture by the study of a large class of matrices in Ω n . Here we prove that this conjecture also holds for another large class of (1, −1)-matrices which are all nonsingular. We also give an upper bound for the permanents of a class of matrices in Ω n which are not all regular.
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References
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Seifter, N. Upper bounds for permanents of (1, − 1)-matrices. Israel J. Math. 48, 69–78 (1984). https://doi.org/10.1007/BF02760525
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DOI: https://doi.org/10.1007/BF02760525