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

Abstract

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.

arXiv commentcorrected an error in the linear description of the permutahedron in introduction

References in corpus (1)

• Symmetry Matters for Sizes of Extended Formulations

Cited by in corpus (3)

• Combinatorial Bounds on Nonnegative Rank and Extended Formulations
• Exponential Lower Bounds for Polytopes in Combinatorial Optimization
• An algebraic approach to symmetric extended formulations