UpDownRuns on Permutation
Maximal monotone runs, with p(1) counted alone when it is a descent.
Called as CombinatorialStat(x, "UpDownRuns"). The head's page has its examples.
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FindStat St000638
The number of up-down runs of a 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] | 2 |
[3,1,2] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000638 has the rest.