# Unexpected result from CycleIndexPolynomial?

Posted 8 months ago
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 In:= CycleIndexPolynomial[SymmetricGroup, {x, x, x}] Out= 1 Shouldn't this be x? I get 1.mathworld .wolfram.com says it is x. Answer
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Posted 8 months ago
 Cycles permutations in WL remove singletons, and therefore the only element of SymmetricGroup is Cycles[{}] instead of Cycles[{{1}}]. This is the source of the mismatch you see.CycleIndexPolynomial takes a third argument to specify the size of the domain of action of the group. Then you can be specific and say In:= CycleIndexPolynomial[SymmetricGroup, {x}, 1] Out= x Answer
Posted 8 months ago
 Thank you Jose. I am now able to include the cycle index for SymmetricGroup in expressing certain integer sequences as a sum of symmetric groups. The calculation below is an example for finding the (N-3)/2 nd term for N = 41 in OEIS A000930In:= AOut= {19, 16, 13, 10, 7, 4, 1}In:= Table[ CycleIndexPolynomial[ SymmetricGroup[A[[k]]], {k, k, k, k, k, k, k, k, k, k, k, k, k, k, k, k, k, k}, A[[k]]], {k, 1, imax + 1}]Out= {1, 17, 105, 286, 330, 126, 7}In:= Total[%]Out= 872 Answer
Posted 8 months ago
 Great! I guess it would be possible to use in general Table[k, Max[A]] instead of the list {k, k, ..., k}. Answer
Posted 8 months ago
 Yes, that helps streamline the command, particularly for large Max[A] . Thanks! Answer