I want the cycle index of the group of automorphisms of a (say 3 X 3) grid graph. I can produce the elements of the group with:
GroupElements[GraphData[{"Grid", {3, 3}}, "AutomorphismGroup"]]
This gives me:
{Cycles[{}], Cycles[{{2, 4}, {3, 7}, {6, 8}}],
Cycles[{{1, 3}, {4, 6}, {7, 9}}],
Cycles[{{1, 3, 9, 7}, {2, 6, 8, 4}}],
Cycles[{{1, 7, 9, 3}, {2, 4, 8, 6}}],
Cycles[{{1, 7}, {2, 8}, {3, 9}}], Cycles[{{1, 9}, {2, 6}, {4, 8}}],
Cycles[{{1, 9}, {2, 8}, {3, 7}, {4, 6}}]}
What I want is something like: $1/8(s_1^9 + 4s_2^3 4s_1^3 + 2s_4^2 s_1 + s_2^4 s_1) $.
The problem seems to be that CycleIndex
Needs["Combinatorica
"]`.
CycleIndexPolynomial
, which is a builtin. $\endgroup$ – Szabolcs Aug 9 '16 at 19:14