置换面体的对称扩张尺寸的紧下界及类似结果
Tight Lower Bounds on the Sizes of Symmetric Extensions of Permutahedra and Similar Results
摘要：
置换面体Pi_n有2^n-2个面。Birkhoff多面体提供了一个大小为Theta（n^2）的Pi_n的对称扩展公式。最近，Goemans描述了一个大小为Theta（nlog（n））的Pi_n的非对称扩展形式.本文证明了Omega（n^2）是Pi_n的对称扩展公式的大小的一个下界.
英文摘要：
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.
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