An Algebraic Approach to Symmetric Extended Formulations

  • Gábor Braun
  • Sebastian Pokutta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)


Extended formulations are an important tool to obtain small (even compact) formulations of polytopes by representing them as projections of higher dimensional ones. It is an important question whether a polytope admits a small extended formulation, i.e., one involving only a polynomial number of inequalities in its dimension. For the case of symmetric extended formulations (i.e., preserving the symmetries of the polytope) Yannakakis established a powerful technique to derive lower bounds and rule out small formulations. We rephrase the technique of Yannakakis in a group-theoretic framework. This provides a different perspective on symmetric extensions and considerably simplifies several lower bound constructions.


symmetric extended formulations polyhedral combinatorics group theory representation theory matching polytope 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gábor Braun
    • 1
  • Sebastian Pokutta
    • 2
  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany
  2. 2.Department of MathematicsFriedrich-Alexander-University of Erlangen-NürnbergErlangenGermany

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