Formulas for the Volumes of the Polytope of Doubly-stochastic Matrices and Its Faces
نویسندگان
چکیده
We provide an explicit combinatorial formula for the volume of the polytope of n× n doubly-stochastic matrices, also known as the Birkhoff polytope. We do this through the description of a generating function for all the lattice points of the closely related polytope of n × n real non-negative matrices with all row and column sums equal to an integer t. We can in fact recover similar formulas for all coefficients of the Ehrhart polynomial of the Birkhoff polytope and for all its faces.
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