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Algorithms, Combinatorics and Optimization Seminar
UIC Title: Discrete metric spaces: global structure, enumeration, and 0-1 laws Abstract: Fix an integer r ≥ 3. Given an integer n, we define Mr(n) to be the set of metric spaces with underlying set {1,..., n} such that the distance between any two points lies in {1,...,r}. We present results describing the approximate structure of these metric spaces when n is large. We then present consequences of these structural results, including an asymptotic enumeration for Mr(n), and in the case when r is even, a first-order labeled 0-1 law. This is joint work with Dhruv Mubayi. Date: Thursday, November 5, 2015 Time: 3:30 pm Location: Wean Hall 8220 Submitted by: Bukh |