Finding fixed points of the kth iteration of the shift map

[goosefrabbas]

Homework Statement

How many points in Σ_N are fixed by σ^k_N?

Homework Equations

σ^k_N is the k^th iteration of the shift map σ_N.

The Attempt at a Solution

I'm not sure where to start. I probably just need a hint.

 

[HallsofIvy]

First, what, exactly, are Σ_N and σ_N? What are their definitions?