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Questions involving results for the special case of matrices over the integers, reals, or complex numbers in which all coefficients are 0 or 1 (e.g. permutation matrices and adjacency matrices of graphs or digraphs).

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Configurations of signs in a matrix under certain conditions

I have a combinatorial question which is out of my research area. Given a $2^k\times 2^k$ matrix $A=[a_{i,j}]$ with entries in $\lbrace0,\pm1\rbrace$, where $k$ is a positive integer. Is it possible …
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Configurations of signs in a matrix under certain conditions

Thank you user21478 and Yemon for your answer/comments. Actually, I observed quite easily that the "nonzero-sharing condition" is not compatible with the condition (1) for a large $k$. Proof. For simp …
Masayoshi Kaneda's user avatar