SignedPermutationOrder on SignedPermutation
The least m >= 1 with p^m the identity, p acting on -n..n.
FindStat's St001555. The lcm of the signed orbit lengths of 1..n: a cycle is counted twice when it is negative. Not PermutationOrder, which reads the word as an unsigned permutation.
Called as CombinatorialStat(x, "SignedPermutationOrder"). The head's page has its examples.
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Distribution
Over SignedPermutations at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001555
The order of a signed permutation.
| Object | Value |
|---|---|
[1] | 1 |
[-1] | 2 |
[1,2] | 1 |
[2,1] | 2 |
[-1,2] | 2 |
[-2,1] | 4 |
[1,-2] | 2 |
[2,-1] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001555 has the rest.