A generating function for all semi-magic squares and the volume of the Birkhoff polytope |
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Authors: | J. A. De Loera F. Liu R. Yoshida |
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Affiliation: | (1) University of California Davis, Davis, CA 95616, USA |
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Abstract: | We present a multivariate generating function for all n×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×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. |
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Keywords: | Birkhoff polytope Volume Lattice points Generating functions Ehrhart polynomials |
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