LongestKOneTwoPattern on Permutation

The largest k such that p has an occurrence of k 1 2 ... (k-1): a first entry above an increasing run of later, smaller ones.

On Permutation

Called as CombinatorialStat(x, "LongestKOneTwoPattern"). 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 St000451

The length of the longest pattern of the form k 1 2.

The length of the longest pattern of the form k 1 2...(k-1).

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000451 has the rest.