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Tight Lower Bounds on the Sizes of Symmetric Extensions of Permutahedra and Similar Results

It is well known that the permutahedron Pi_n has 2^n-2 facets. The Birkhoff polytope provides a symmetric extended formulation of Pi_n of size Theta(n^2). Recently, Goemans described a non-symmetric extended formulation of Pi_n of size Theta(n log(n)). In this paper, we prove that Omega(n^2) is a lower bound for the size of symmetric extended formulations of Pi_n.

preprint2013arXivOpen access
Kanstantsin Pashkovich
math.COmath.OC
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Kanstantsin Pashkovich

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