Subseturi disjuncte

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Filip Chindea
Newton
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Joined: Thu Sep 27, 2007 9:01 pm
Location: Bucharest

Subseturi disjuncte

Post by Filip Chindea »

Fie un numar real pozitiv \( \alpha < \left(3 - \sqrt{5}\right)/2 \). Sa se arate ca exista intregii pozitivi \( n \) si \( p > \alpha \cdot 2^{n} \) astfel incat putem selecta \( 2p \) subseturi distincte \( S_1, ..., S_p, T_1, ..., T_p \subseteq \overline{1, n} \) cu orice \( S_i \) diferit de oricare \( T_j \).

[ IMO Shortlist 2007, C7 ]
Life is complex: it has real and imaginary components.
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