A Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff Polytope
Combinatorics
2008-10-09 v2
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.
Cite
@article{arxiv.math/0701866,
title = {A Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff Polytope},
author = {Jesus A. De Loera and Fu Liu and Ruriko Yoshida},
journal= {arXiv preprint arXiv:math/0701866},
year = {2008}
}
Comments
24 pages, 1 figure. To appear in Journal of Algebraic Combinatorics