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Miklós Schweitzer 1986, Problem 2

Source:

September 12, 2016
Miklos Schweitzercollege contestslinear algebramatrixcombinatorics

Problem Statement

Show that if k≤n2k\leq \frac n2 and F\mathcal F is a family k×kk\times k submatrices of an n×nn\times n matrix such that any two intersect then ∣F∣≤(n−1k−1)2|\mathcal F|\leq \binom{n-1}{k-1}^2 [Gy. Katona]
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