Abstract Algebra: Theory and Applications · Problem 14.5.15

The Sylow Theorems — Thomas Judson

Mathematics — Abstract Algebra · burnside-coloring-hexagon

Problem

Suppose that the vertices of a regular hexagon are to be colored either red or white. How many ways can this be done up to a symmetry of the hexagon? Hint. (1⋅26+3⋅24+4⋅23+2⋅22+2⋅21)/12=13(1 \cdot 2^6 + 3 \cdot 2^4 + 4 \cdot 2^3 + 2 \cdot 2^2 + 2 \cdot 2^1)/12 = 13.

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