Counting Integer Points in Multi-Index Transportation Polytopes

TL;DR

This paper develops asymptotic formulas for counting integer and binary points in multi-index transportation polytopes, providing a simple approximation as the dimensions grow large, extending previous results in the field.

Contribution

It generalizes existing results to a broader class of multi-index transportation polytopes and offers a closed-form approximation for large dimensions.

Findings

Derived asymptotic formulas for integer points

Provided a simple closed-form approximation for large dimensions

Extended previous work of Barvinok and Hartigan

Abstract

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.