OneBoxPatterns on Permutation

Positions i with a neighbouring entry, left or right, differing from p(i) by exactly 1.

On Permutation

Called as CombinatorialStat(x, "OneBoxPatterns"). 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 St000064

The number of one-box pattern of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000064 has the rest.