Combinatorics by Loehr Nicholas;

Author:Loehr, Nicholas; [Loehr, Nicholas;]
Language: eng
Format: epub
ISBN: 9781498780254
Publisher: CRC Press
Published: 2017-09-15T00:00:00+00:00

So the associativity axiom holds, completing the proof that is a group action.

The following theorem is the formal enunciation of our earlier claim that group actions and permutation representations are essentially the same thing.

7.77. Theorem: Equivalence of Group Actions and Permutation Representations. group actions!and permutation representations permutation representations!and group actions Fix a group G and a set X. Let A be the set of all group actions of G on X, and let P be the set of all permutation representations of G on X. There are mutually inverse bijections and , given by

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