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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 …
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Assuming an unpublished Ramsey-type result by Robertson and Seymour about Kuratowski minors [FK18, Claim 5], which is now "folklore" in the graph-minor community,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 …