Counting Integer Points in Multi-Index Transportation Polytopes

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 $k_1\times k_2\times \dots \times k_{\nu }$ transportation polytopes. A simple closed form approximation is given as the $k_j$s go to infinity.

38 pages

References in corpus (2)

• On the complexity of computing Kronecker coefficients
• Approximate counting of regular hypergraphs

Cited by in corpus (3)

• Bounds on the Kronecker coefficients
• Lower bounds for contingency tables via Lorentzian polynomials
• Upper bounds on Kronecker coefficients with few rows