InsertionBumpsOfOne on Permutation

One more than the longest decreasing subsequence of the entries before 1.

On Permutation

Inserting 1 bumps along the first column of the tableau built from the entries before it.

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

Live

Distribution

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

Sizes 1 to

FindStat St001390

The number of bumps occurring when Schensted-inserting the letter 1 of a permutation.

Object	Value
[1]	1
[1,2]	1
[2,1]	2
[1,2,3]	1
[1,3,2]	1
[2,1,3]	2
[2,3,1]	2
[3,1,2]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001390 has the rest.