ReducedReflectionLength on Permutation
The total displacement less the inversions.
Twice the depth less the length.
Called as CombinatorialStat(x, "ReducedReflectionLength"). The head's page has its examples.
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FindStat St000809
The reduced reflection length of the permutation.
| Object | Value |
|---|---|
[1,2] | 0 |
[2,1] | 1 |
[1,2,3] | 0 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 2 |
[3,1,2] | 2 |
[3,2,1] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000809 has the rest.