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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 …