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AscentBottomSum on Permutation ​

The sum of the ascent bottoms: p(i) over the ascents i.

On Permutation

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

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Distribution

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FindStat St000472

The sum of the ascent bottoms of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000472 has the rest.