Minimizing the permanent over some faces of the polytope of doubly stochastic matrices
نویسندگان
چکیده
منابع مشابه
The polytope of even doubly stochastic matrices
The polytope Q, of the convex combinations of the permutation matrices of order n is well known (Birkhoff’s theorem) to be the polytope of doubly stochastic matrices of order n. In particular it is easy to decide whether a matrix of order n belongs to Q,. . check to see that the entries are nonnegative and that all row and columns sums equal 1. Now the permutations z of { 1, 2, . . . . n} are i...
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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 f...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)00214-k