  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.
