The University of Michigan Combinatorics Seminar


Abstract 

I plan to discuss a rather simple and computationally efficient formula for the number of integer points in a higherdimensional polytope. The underlying intuition is based on the maximum entropy principle and the local Central Limit Theorem. One can prove that the formula is asymptotically exact in a wide variety of situations, including, in particular, counting integer points in multiway transportation polytopes. To count integer points in a twoway transportation polytope (that is, to count nonnegative integer matrices with prescribed row and column sums), one has to introduce the Edgeworth correction factor, which is also efficiently computable. This is a joint work with J.A. Hartigan (Yale). 