CyclePeaks on Permutation
Values i with p^-1(i) < i > p(i).
Every cycle has as many peaks as valleys, so this is the cycle valleys too.
Called as CombinatorialStat(x, "CyclePeaks"). The head's page has its examples.
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FindStat St000994
The number of cycle peaks and the number of cycle valleys of a permutation.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[1,2] | 0 |
[2,1] | 1 |
[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/St000994 has the rest.