RecursiveStartMinimumCount on Permutation
FindStat's aix: the number of times, peeling the word, the minimum of what is left is its first entry.
Recursively: the minimum first counts one and the rest is the word without it; the minimum last ends the walk; otherwise the walk goes on with the entries before the minimum (St000873).
Called as CombinatorialStat(x, "RecursiveStartMinimumCount"). The head's page has its examples.
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FindStat St000873
The aix 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] | 0 |
[3,1,2] | 1 |
[3,2,1] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000873 has the rest.