I have some solutions, but it felt way too easy, so I am pretty sure I am missing something and would like to check my understanding of the problem:
First of all, for the RPS(5) game, is the "permutation" that changes none of the labels also counted as an automorphism or not? I only found 4 permutations that change at least one of the labels for the given example.
I am also confused by how the permutations are defined and what permutations are actually allowed in this case. Let's assume I have a permutation that relabels the numbers as follows:
0 to 1
1 to 2
2 to 0
3 to 4
4 to 3
I can't define this permutation in a single list. If we draw this in a graph, we get a disconnected graph with two cycles. Are we limited to permutations that result in a single cycle?
