We give compact extended formulations for the packing and partitioning
orbitopes (with respect to the full symmetric group) described and analyzed in
(Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all
0/1-matrices with lexicographically sorted columns and at most, resp. exactly,
one 1-entry per row. They are important objects for symmetry reduction in
certain integer programs.
Using the extended formulations, we also derive a rather simple proof of the
fact that basically shifted-column inequalities suffice in order to describe
those orbitopes linearly.Comment: 16 page