Skip to main content
A Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff
Polytope
Published Web Location
https://arxiv.org/pdf/math/0701866.pdfNo data is associated with this publication.
Abstract
We present a multivariate generating function for all n x n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semi-magic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of the polytope B_n of n x n doubly-stochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of B_n and any of its faces.