对称扩展公式的代数方法
An algebraic approach to symmetric extended formulations
摘要：
扩展公式是一个重要的工具，以获得小（甚至紧凑）配方的多面体表示为高维的投影。这是一个重要的问题，一个多面体是否允许一个小的扩展公式，即，一个只涉及其维数的多项式不等式。对于对称扩展公式的情况（即，保持多面体的对称性）Yannakakis建立了一个强大的技术来推导下限和排除小公式。我们重新措辞的技术Yannakakis在群论框架。这提供了一个不同的角度对对称扩张，并大大简化了几个下界的建设。
英文摘要：
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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