Abstract
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.
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Braun, G., Pokutta, S. (2012). An Algebraic Approach to Symmetric Extended Formulations. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds) Combinatorial Optimization. ISCO 2012. Lecture Notes in Computer Science, vol 7422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_14
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DOI: https://doi.org/10.1007/978-3-642-32147-4_14
Publisher Name: Springer, Berlin, Heidelberg
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