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VeryBigAscents on Permutation ​

Positions i with p(i+1) - p(i) > 2.

On Permutation

Called as CombinatorialStat(x, "VeryBigAscents"). The head's page has its examples.

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Distribution

Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.

FindStat St000871

The number of very big ascents of a permutation.

ObjectValue
[]0
[1]0
[1,2]0
[2,1]0
[1,2,3]0
[1,3,2]0
[2,1,3]0
[2,3,1]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000871 has the rest.