RecursiveEndMaximumCount on Permutation
FindStat's rix: the number of times, peeling the word, the maximum of what is left is its last entry.
Recursively: the maximum last counts one and the rest is the word without it; the maximum first ends the walk; otherwise the walk goes on with the entries after the maximum (St000461).
Called as CombinatorialStat(x, "RecursiveEndMaximumCount"). The head's page has its examples.
Live
Distribution
Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.
FindStat St000461
The rix statistic of a permutation.
| Object | Value |
|---|---|
[1,2] | 2 |
[2,1] | 0 |
[1,2,3] | 3 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 1 |
[3,1,2] | 0 |
[3,2,1] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000461 has the rest.