Abstract Algebra: Theory and Applications · Problem 14.5.17

The Sylow Theorems — Thomas Judson

Mathematics — Abstract Algebra · switching-functions-equivalence-classes

Problem

How many equivalence classes of switching functions are there if the input variables x1x_1, x2x_2, and x3x_3 can be permuted by any permutation in S3S_3? What if the input variables x1,x2,x3x_1, x_2, x_3, and x4x_4 can be permuted by any permutation in S4S_4? Hint. (1⋅28+3⋅26+2⋅24)/6=80(1 \cdot 2^8 + 3 \cdot 2^6 + 2 \cdot 2^4)/6 = 80.

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