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We give compact extended formulations for the packing and partitioningorbitopes (with respect to the full symmetric group) described and analyzed in(Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all0/1-matrices with lexicographically sorted columns and at most, resp. exactly,one 1-entry per row. They are important objects for symmetry reduction incertain integer programs.  Using the extended formulations, we also derive a rather simple proof of thefact that basically shifted-column inequalities suffice in order to describethose orbitopes linearly.

Extended Formulations for Packing and Partitioning Orbitopes