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    Permutations : Parity

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    Show that $ and %$%^-1 have the same parity for all % and $ in Sn. (Sn is the symmetric group of degree n)

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    Solution Preview

    We know for any %, % and % have the same parity.
    Now we define sgn$=1 if $ ...

    Solution Summary

    Parity in a symmetric group is concisely proven.