ACO The ACO Seminar (2015–2016)

Nov. 5, 3:30pm, Wean 8220
Caroline Terry, UIC
Discrete metric spaces: global structure, enumeration, and 0-1 laws


Fix an integer r3. 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.

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