An Asymptotic Formula for the Number of Integer Points in Multi-Index Transportation Polytopes

David Benson-Putnins

Published 2014-02-19, updated 2014-09-17Version 2

For a wide class of $k_1\times k_2....\times k_{\nu}$ multi-index transportation polytopes, we count the number of integer points contained in them. A simple closed form approximation is given whose relative error is asymptotically zero as the $k_j$s go to infinity.