Identifier
Values
[1] => [1,0,1,0] => [2,1] => 0
[2] => [1,1,0,0,1,0] => [1,3,2] => 0
[1,1] => [1,0,1,1,0,0] => [2,1,3] => 0
[3] => [1,1,1,0,0,0,1,0] => [1,2,4,3] => 0
[2,1] => [1,0,1,0,1,0] => [2,3,1] => 0
[1,1,1] => [1,0,1,1,1,0,0,0] => [2,1,3,4] => 0
[4] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 0
[3,1] => [1,1,0,1,0,0,1,0] => [3,1,4,2] => 1
[2,2] => [1,1,0,0,1,1,0,0] => [1,3,2,4] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [2,4,1,3] => 0
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => 0
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => 0
[3,2] => [1,1,0,0,1,0,1,0] => [1,3,4,2] => 0
[3,1,1] => [1,0,1,1,0,0,1,0] => [2,1,4,3] => 0
[2,2,1] => [1,0,1,0,1,1,0,0] => [2,3,1,4] => 0
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => 1
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 1
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => 0
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => 0
[3,2,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 1
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => 0
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => 0
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => 0
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 0
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 1
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 0
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => 0
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => 0
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 0
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 0
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 1
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => 0
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => 0
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => 1
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 1
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 0
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 0
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => 1
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of strict 3-descents.
A strict 3-descent of a permutation $\pi$ of $\{1,2, \dots ,n \}$ is a pair $(i,i+3)$ with $ i+3 \leq n$ and $\pi(i) > \pi(i+3)$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.