Maximum entropy Edgeworth estimates of the number of integer points in polytopes

Alexander Barvinok, J. A. Hartigan

Abstract: The number of points $x=(x_1,x_2,...x_n)$ that lie in an integer cube $C$ in $R^n$ and satisfy the constraints ${\sum }_j{h}_{ij}(x_j)=s_i,1\le i\le d$ is approximated by…