Burnside theorem & polyA Theorem

Source: Internet
Author: User
Burnside theorem & polyA Theorem
  1. Replacement:

    Replacement is to exchange the dyeing of n elements to generate a new dyeing scheme.

  2. GROUP:

    The Set g of an element and a binary operation (*) constitute a group. The group meets the following requirements:

    1. Closed:\ (\ Forall a, B \ in G, \ exists c \ in G, C = a * B \)

    2. Combination law:\ (\ Forall A, B, C, (a * B) * C = A * (B * C )\)

    3. Unit RMB:\ (\ Exists e \ in G, \ forall A, A * E = E * A = \)

    4. Reverse element:\ (\ Forall A \ in G, \ exists B \ in G, a * B = B * A = E, B = a ^ {-1 }\)

  3. Replacement group:

    That is, for the group of the replaced set, the binary operation is the replacement connection, that is, the replacement of a replaced scheme after a dyeing scheme.

Burnside theorem & polyA Theorem

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