Successions on Permutation
Positions i with p(i+1) = p(i) + 1.
Also called small ascents or 1-rises.
Called as CombinatorialStat(x, "Successions"). The head's page has its examples.
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Distribution
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Also on
The same name on other carriers, each its own implementation: SetPartition.
FindStat St000441
The number of successions of a permutation.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[1,2] | 1 |
[2,1] | 0 |
[1,2,3] | 2 |
[1,3,2] | 0 |
[2,1,3] | 0 |
[2,3,1] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000441 has the rest.