A Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff Polytope

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dc.creatorDe Loera, Jesus A.
dc.creatorLiu, Fu
dc.creatorYoshida, Ruriko
dc.date2007-01-30
dc.date2008-10-09
dc.date.accessioned2026-07-07T10:08:36Z
dc.date.available2026-07-07T10:08:36Z
dc.descriptionWe 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.
dc.description24 pages, 1 figure. To appear in Journal of Algebraic Combinatorics
dc.identifierhttps://arxiv.org/abs/math/0701866
dc.identifierhttp://arxiv.org/abs/math/0701866
dc.identifierdoi:10.1007/s10801-008-0155-y
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171051
dc.subjectCombinatorics
dc.subject52C07; 52B20
dc.titleA Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff Polytope
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