MathDB
Miklos Schweitzer 1969_11

Source:

October 15, 2008
combinatorics proposedcombinatorics

Problem Statement

Let A1,A2,... A_1,A_2,... be a sequence of infinite sets such that ∣Ai∩Aj∣≤2 |A_i \cap A_j| \leq 2 for i \not\equal{}j. Show that the sequence of indices can be divided into two disjoint sequences i1<i2<... i_1<i_2<... and j1<j2<... j_1<j_2<... in such a way that, for some sets E E and F F, |A_{i_n} \cap E|\equal{}1 and |A_{j_n} \cap F|\equal{}1 for n\equal{}1,2,... . P. Erdos
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