Counting Integer Points in Multi-Index Transportation Polytopes
  We expand on a result of Barvinok and Hartigan to derive asymptotic formulas for the number of integer and binary integer points in a wide class of multi-index $k_1\times k_2\times \ldots \times k_{\nu}$ transportation polytopes. A simple closed form approximation is given as the $k_j$s go to infinity. 
David Benson-Putnins
math.CO math.MG