AlternatingRuns on Permutation
The interior peaks plus the interior valleys.
FindStat's title: the times the word switches from increasing to decreasing or back.
Called as CombinatorialStat(x, "AlternatingRuns"). The head's page has its examples.
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FindStat St000483
The number of times a permutation switches from increasing to decreasing or decreasing to increasing.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[1,2] | 0 |
[2,1] | 0 |
[1,2,3] | 0 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000483 has the rest.