Asymptotics of the number of lattice points in the transportation polytope

Thomas Lee (University of Waterloo)

Counting the number of lattice points of the transportation polytope is of interest in a variety of domains, including statistics, group theory, design theory, and graph theory. In this talk, we discuss how earlier bounds derived by Brändén, Leake, and Pak (2023) are log-asymptotically correct under given conditions. When symmetry exists, improved conditions are given for log-asymptotic correctness. Finally, we show examples where our conditions either hold, do not hold but log-asymptotic correctness holds, or do not hold and log-asymptotic correctness fails.

 Overview  Program