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Group Actions on Boolean Algebras

  • Richard P. Stanley
Chapter
  • 5.3k Downloads
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Let us begin by reviewing some facts from group theory. Suppose that X is an n-element set and that G is a group. We say that Gacts on the set X if for every element π of G we associate a permutation (also denoted π) of X, such that for all xX and π,σG we have
$$\displaystyle{\pi (\sigma (x)) = (\pi \sigma )(x).}$$
Thus [why?] an action of G on X is the same as a homomorphism

Keywords

Quotient Poset Symmetric Chain Decomposition Edge Reconstruction Conjecture Sperner Property Vertex Permutation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Richard P. Stanley
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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