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For question borderline with, or having application to, computer science. Consider also posting http://cs.stackexchange.com/ or http://cstheory.stackexchange.com/ instead of here, if appropriate.

2 votes

Maximum number of $0$-$1$ vectors with a given rank

A construction for the lower bound: take the matrix of rank $k-1$ with $2^{k-1}$ columns consisting of all $\{0,1\}$-combinations of the vectors $e_1+e_2, e_3+e_4 \dots, e_{2k-3}+e_{2k-2}$. Then add t …
Jan Kyncl's user avatar
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45 votes

Issue UPDATE: in graph theory, different definitions of edge crossing numbers - impact on ap...

Assuming an unpublished Ramsey-type result by Robertson and Seymour about Kuratowski minors [FK18, Claim 5], which is now "folklore" in the graph-minor community, an asymptotic variant of the crossing …
Jan Kyncl's user avatar
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