Journal ArticleDOI
On permanents of (1, − 1)-matrices
TLDR
A preliminary study on permanents of (1, − 1)-matrices is given in this paper, where some inequalities are derived and a few unsolved problems are mentioned, believed to be new.Abstract:
A preliminary study on permanents of (1, − 1)-matrices is given. Some inequalities are derived and a few unsolved problems, believed to be new, are mentioned.read more
Citations
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An update on Minc's survey of open problems involving permanents
Gi-Sang Cheon,Ian M. Wanless +1 more
TL;DR: In this paper, the progress made since 1986 on the conjectures and open problems listed in H. Minc's survey articles on the theory of permanents is summarised and discussed.
Journal ArticleDOI
Upper bounds for permanents of (1, − 1)-matrices
TL;DR: In this paper, it was shown 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 Ωn.
Journal ArticleDOI
Permanents of matrices of signed ones
TL;DR: In this article, the permanents for all Hadamard matrices of orders up to and including 28 were calculated and the lowest positive value taken by the permanent in these cases was established.
Journal ArticleDOI
On some questions concerning permanents of (1,-1) matrices
TL;DR: In this paper, the problem of finding nonsingular matrices in a set of alln×n-(1,−1)-matrices with power n ≥ 6 was studied and a solution for n≦6 was presented.
Journal ArticleDOI
On (+1,-1)-matrices with vanishing permanent
Rodica Simion,Frank Schmidt +1 more
TL;DR: It is shown that if A is an nxn (+1,-1)-matrix and if n = 2^m-1 for some positive integer m, then per (A) 0.
References
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A Survey of Matrix Theory and Matrix Inequalities.
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Combinatorics: room squares, sum-free sets, Hadamard matrices
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