Identifier
Values
[1,0] => [2,1] => [2,1] => [2,1] => 0
[1,0,1,0] => [3,1,2] => [3,1,2] => [2,3,1] => 0
[1,1,0,0] => [2,3,1] => [3,2,1] => [3,1,2] => 1
[1,0,1,0,1,0] => [4,1,2,3] => [4,1,2,3] => [2,3,4,1] => 0
[1,0,1,1,0,0] => [3,1,4,2] => [4,3,1,2] => [2,4,1,3] => 1
[1,1,0,0,1,0] => [2,4,1,3] => [4,2,1,3] => [3,1,4,2] => 1
[1,1,0,1,0,0] => [4,3,1,2] => [3,1,4,2] => [3,4,1,2] => 2
[1,1,1,0,0,0] => [2,3,4,1] => [4,3,2,1] => [4,1,2,3] => 3
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5,1,2,3,4] => [2,3,4,5,1] => 0
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,4,1,2,3] => [2,3,5,1,4] => 1
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [5,3,1,2,4] => [2,4,1,5,3] => 1
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [4,1,2,5,3] => [2,4,5,1,3] => 2
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,4,3,1,2] => [2,5,1,3,4] => 3
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [5,2,1,3,4] => [3,1,4,5,2] => 1
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5,4,2,1,3] => [3,1,5,2,4] => 2
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [3,1,5,2,4] => [3,4,1,5,2] => 2
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [4,1,5,2,3] => [4,3,5,1,2] => 3
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [3,1,5,4,2] => [3,5,1,2,4] => 4
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,3,2,1,4] => [4,1,2,5,3] => 3
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,2,1,5,3] => [4,1,5,2,3] => 4
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [4,3,1,5,2] => [4,5,1,3,2] => 4
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,4,3,2,1] => [5,1,2,3,4] => 6
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,5,1,2,3,4] => [2,3,4,6,1,5] => 1
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [6,4,1,2,3,5] => [2,3,5,1,6,4] => 1
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [5,1,2,3,6,4] => [2,3,5,6,1,4] => 2
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,5,4,1,2,3] => [2,3,6,1,4,5] => 3
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [6,3,1,2,4,5] => [2,4,1,5,6,3] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,5,3,1,2,4] => [2,4,1,6,3,5] => 2
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [4,1,2,6,3,5] => [2,4,5,1,6,3] => 2
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [5,1,2,6,3,4] => [2,5,4,6,1,3] => 3
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [4,1,2,6,5,3] => [2,4,6,1,3,5] => 4
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [6,4,3,1,2,5] => [2,5,1,3,6,4] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [5,3,1,2,6,4] => [2,5,1,6,3,4] => 4
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [5,4,1,2,6,3] => [2,5,6,1,4,3] => 4
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,5,4,3,1,2] => [2,6,1,3,4,5] => 6
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [3,1,4,5,6,2] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [6,5,2,1,3,4] => [3,1,4,6,2,5] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [6,4,2,1,3,5] => [3,1,5,2,6,4] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [5,2,1,3,6,4] => [3,1,5,6,2,4] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,5,4,2,1,3] => [3,1,6,2,4,5] => 4
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [3,4,1,5,6,2] => 2
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [3,1,6,5,2,4] => [3,4,1,6,2,5] => 3
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,1,6,2,3,5] => [4,3,5,1,6,2] => 3
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [6,1,5,2,3,4] => [5,3,4,6,2,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,1,6,5,2,3] => [4,3,6,1,2,5] => 5
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [3,1,6,4,2,5] => [3,5,1,2,6,4] => 4
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [3,1,5,2,6,4] => [3,5,1,6,2,4] => 5
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [5,4,1,6,2,3] => [5,3,6,1,4,2] => 6
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [3,1,6,5,4,2] => [3,6,1,2,4,5] => 7
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [6,3,2,1,4,5] => [4,1,2,5,6,3] => 3
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,5,3,2,1,4] => [4,1,2,6,3,5] => 4
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [4,2,1,6,3,5] => [4,1,5,2,6,3] => 4
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [5,2,1,6,3,4] => [5,1,4,6,2,3] => 6
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [4,2,1,6,5,3] => [4,1,6,2,3,5] => 6
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [4,3,1,6,2,5] => [4,5,1,3,6,2] => 4
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,3,1,6,2,4] => [5,4,1,6,3,2] => 4
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => 9
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,3,1,6,5,2] => [4,6,1,3,2,5] => 7
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,4,3,2,1,5] => [5,1,2,3,6,4] => 6
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,3,2,1,6,4] => [5,1,2,6,3,4] => 7
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [5,4,2,1,6,3] => [5,1,6,2,4,3] => 7
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,4,3,1,6,2] => [5,6,1,3,4,2] => 8
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,5,4,3,2,1] => [6,1,2,3,4,5] => 10
[] => [1] => [1] => [1] => 0
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
click to show known generating functions       
Description
The number of occurrences of the pattern 312 in a permutation.
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.