Please join the Department of Mathematics and Statistics on Monday, October 11th at 3:30pm in Votey Hall 209 for a fascinating combinatorics seminar featuring our very own, Professor Greg Warrington.
A Combinatorial Variant of Sylvester's Four-Point Problem
Professor Greg Warrington, University of Vermont
Monday, October 11th, 3:30PM, Votey Hall 209
Abstract: In 1864, J. J. Sylvester posed his Four-Point Problem: What is the probability that four points chosen at random from a region R have a quadrilateral as their convex hull? If R is convex, the answer has been shown to range between 2/3 and 0.704, depending on the particular region R. I'll use a beautiful combinatorial classification of points in the plane due to Goodman and Pollack to relate Sylvester's question to a question about permutations. The answer to this combinatorial version of the problem is now known (due to the efforts of O. Angel and A. E. Holroyd) to be 3/4.