LexicographicRank on Permutation
The position of p among the permutations of its size in lexicographic order, counting from 1.
One more than the Lehmer code read as a number in the factorial base.
Called as CombinatorialStat(x, "LexicographicRank"). The head's page has its examples.
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Distribution
Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.
FindStat St000020
The rank of the permutation.
| Object | Value |
|---|---|
[1] | 1 |
[1,2] | 1 |
[2,1] | 2 |
[1,2,3] | 1 |
[1,3,2] | 2 |
[2,1,3] | 3 |
[2,3,1] | 4 |
[3,1,2] | 5 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000020 has the rest.