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COMMENTS
| It is conjectured by Kraeuter and Seifter that for n >= 5 the maximal permanent of a nonsingular n X n (+1,-1)-matrix is attained by a matrix with exactly n-1 -1's on the diagonal (compare A087981).
The maximal possible value for the permanent of a singular n X n (+1,-1)-matrix is obviously n!.
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REFERENCES
| A. R. Kraeuter and N. Seifter, Some properties of the permanent of (1,-1)-matrices, Linear and Multilinear Algebra 15 (1984), 207-223.
N. Seifter, Upper bounds for permanents of (1,-1)-matrices, Israel J. Math. 48 (1984), 69-78.
Edward Tzu-Hsia Wang, On permanents of (1,-1)-matrices, Israel J. Math. 18 (1974), 353-361.
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