MathDB

Let \alpha < \frac {3 \minus{} \sqrt {5}}{2} be a positive real number. Prove that there exist positive integers

n

and

p > \alpha \cdot 2^n

for which one can select

2 \cdot p

pairwise distinct subsets

S_1, \ldots, S_p, T_1, \ldots, T_p

of the set

\{1,2, \ldots, n\}

such that

S_i \cap T_j \neq \emptyset

for all

1 \leq i,j \leq p

Author: Gerhard Wöginger, Austria

Problem Statement