Burnside theorem & polyA Theorem

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