- #1
Ted123
- 446
- 0
Homework Statement
Let [itex]G=D_4[/itex] (the group of symmetries (reflections/rotations) of a square) and let [tex]X=\{ \text{colourings of the edges of a square using the colours red or blue} \}[/tex] so a typical element of X is:
What is the size of [itex]X[/itex]?
Let [itex]G[/itex] act on X in the obvious way. You are given that [itex]G[/itex] has 6 orbits on X. Find a representative for each [itex]G[/itex]-orbit, and its size.
The Attempt at a Solution
Obviously there are going to be various ways of colouring the edges of a square, but how can I be sure that I have them all or is there a quicker way to find the size?
How do I find a representative for each G-orbit?