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This week I'm at SODA; proceedings at
doi.org/10.1137/1.978161197548

My favorite talk today was "Extremal and probabilistic results for order types", doi.org/10.1137/1.978161197548
Its main results are (1) the probability that a random point set has a specific order type is upper and lower bounded by functions of the smallest size of a grid containing the order type, and (2) every nontrivial hereditary property of point sets has probability 1/exp(Theta(n log n)) of being true of random point sets.

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