MIT Combinatorics Seminar

Packing cubes in a torus

Tom Bohman  (Carnegie Mellon University)

Friday, March 16, 2007    4:15 pm    Room 2-136


We consider the following packing problem. How many d-dimensional cubes of side length 2 can we pack into a d-dimensional torus of odd side length? In this talk we present some of the best known constructions, detail the connection between this packing problem and the problem of determining the Shannon capacities of graphs, and discuss some recent techniques for establishing upper bounds.