13 hours later…
3:22 PM
> Imagine a pond with small yellow frogs on one end, and large green frogs on the other. After observing the frogs for decades, herpetologists conjecture that the populations represent two distinct species with different evolutionary histories, and are not interfertile. Everyone realizes that to disprove this hypothesis, all it would take would be a single example of a green/yellow hybrid.
> Since (for some reason) the herpetologists really care about this question, they undertake a huge program of breeding experiments, putting thousands of yellow female frogs next to green male frogs (and vice versa) during mating season, with candlelight, soft music, etc. Nothing.
@YuvalFilmus I think the numbers are ok for us to graduate. The limiting point is that graduated sites have their own design and Stack Exchange lacks designer manpower, though they've recruited a second one so it should be better now. Personal Finance & Money and The Workplace graduated recently with slightly fewer questions per day but more traffic. What makes me hesitate on graduation is that we're good with CS undergraduate topics, algorithms and programming language theory but have very little coverage of most applied topics. — Gilles 5 hours ago
6 hours later…
9:59 PM
In combinatorics, the Erdős–Ko–Rado theorem of Paul Erdős, Chao Ko, and Richard Rado is a theorem on intersecting set families. It is part of the theory of hypergraphs, specifically, uniform hypergraphs of rank r.
The theorem is as follows. If n\geq2r and A is a family of distinct subsets of \{1,2,...,n\} such that each subset is of size r and each pair of subsets intersects, then the maximum number of sets that can be in A is given by the binomial coefficient
:\binom{n-1}{r-1}.
(Since a family of sets may be called a hypergraph, and since every set in A has size r, A is a uniform hyper...
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