Timeline for The maximal size of intersection of two sets
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 10, 2018 at 2:18 | vote | accept | zbh2047 | ||
| Nov 10, 2018 at 2:03 | comment | added | zbh2047 | Thank you very much. The first and third question have been solved using your sulution. Also, it can be used to solve question 2. Let $x$ be the number of pairs $(i,j)$ such that $|S_i \cap S_j|\ge (n-1)/2$, then $xn+\left(\binom{n+1}{2}-x\right)\frac {n-3} 2 \ge \frac{{{n^2}(n - 1)(n + 1)}}{{4n}}$. Solving $x$ leads to $x \geqslant \frac{{n(n + 1)}}{{n + 3}}$, namely $x=\Omega(n)$. | |
| Nov 9, 2018 at 20:35 | history | edited | Vlad Matei | CC BY-SA 4.0 |
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| Nov 9, 2018 at 15:50 | history | answered | Vlad Matei | CC BY-SA 4.0 |