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Part of 1968 Miklós Schweitzer

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Miklos Schweitzer 1968_8

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10/8/2008
Let n n and k k be given natural numbers, and let A A be a set such that ∣A∣≤n(n+1)k+1. |A| \leq \frac{n(n+1)}{k+1}. For i=1,2,...,n+1 i=1,2,...,n+1, let Ai A_i be sets of size n n such that ∣Ai∩Aj∣≤k  (i≠j) , |A_i \cap A_j| \leq k \;(i \not=j)\ , A=⋃i=1n+1Ai. A= \bigcup_{i=1}^{n+1} A_i. Determine the cardinality of A A. K. Corradi
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