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Jul 31, 2014 at 11:07 vote accept Zur Luria
Jul 18, 2014 at 12:40 answer added Max Alekseyev timeline score: 5
Jul 12, 2014 at 20:56 comment added Lucia Actually, as noted in my earlier answer the upper bound $\binom{n}{s+1}/\binom{r}{s+1}$ is easy to obtain. I don't know if this is enough, or if you're looking for stronger bounds. Non-trivial can be vague!
Jul 12, 2014 at 20:45 comment added Lucia See my answer to this earlier MO question: mathoverflow.net/questions/161159/… . In particular, the paper by Frankl that I linked discusses general such problems, and Theorem 4.3 there (by Deza, Erdos and Frankl) would give non-trivial bounds in your question.
Jul 12, 2014 at 20:27 history asked Zur Luria CC BY-SA 3.0