Timeline for Simpler lower bound for couples of disjoint sets

7 events

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Oct 19, 2023 at 7:09	comment	added	Ilya Bogdanov		Some example: if $n=q^2+q+1$ and $m=q+1$, you may consider a projective plane over $\mathbb F_q$ and set $\mathcal A_i$ to be the set of pairs of points on the $i$th line. This way you get only $n{q+1\choose 2}{q-1\choose 2}/2<n^3/8$ pairs.
Oct 19, 2023 at 7:05	comment	added	Ilya Bogdanov		If $m$ is much smaller than $n$, your example is surely not the best, as you can move one set from $\mathcal A_m$ to $\mathcal A_{m-1}$ losing $n-m-2\choose 2$ pairs but gaining only $n-m-2$ ones.
Oct 6, 2023 at 14:07	history	edited	Fabius Wiesner	CC BY-SA 4.0	added 109 characters in body
Oct 3, 2023 at 6:04	history	edited	Fabius Wiesner	CC BY-SA 4.0	added 79 characters in body
Oct 2, 2023 at 8:19	history	edited	Fabius Wiesner	CC BY-SA 4.0	added 111 characters in body
Oct 1, 2023 at 21:52	history	edited	Fabius Wiesner	CC BY-SA 4.0	added 112 characters in body
Oct 1, 2023 at 21:27	history	asked	Fabius Wiesner	CC BY-SA 4.0