ValleysIncludingBoundary on Permutation
Positions lower than both neighbours, a larger entry standing off each end.
Excluding the boundary is Valleys.
Called as CombinatorialStat(x, "ValleysIncludingBoundary"). The head's page has its examples.
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FindStat St000099
The number of valleys of a permutation, including the boundary.
| Object | Value |
|---|---|
[1] | 1 |
[1,2] | 1 |
[2,1] | 1 |
[1,2,3] | 1 |
[1,3,2] | 2 |
[2,1,3] | 1 |
[2,3,1] | 2 |
[3,1,2] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000099 has the rest.