CyclicValleys on Permutation
Positions lower than both neighbours, reading the word cyclically.
As many cyclic peaks as cyclic valleys, so this is both.
Called as CombinatorialStat(x, "CyclicValleys"). The head's page has its examples.
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FindStat St000243
The number of cyclic valleys and cyclic peaks of a permutation.
| Object | Value |
|---|---|
[1,2] | 1 |
[2,1] | 1 |
[1,2,3] | 1 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 1 |
[3,1,2] | 1 |
[3,2,1] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000243 has the rest.