Identifier
Values
[1,0] => [1,0] => [1] => 1
[1,0,1,0] => [1,1,0,0] => [1,2] => 2
[1,1,0,0] => [1,0,1,0] => [2,1] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [1,2,3] => 6
[1,0,1,1,0,0] => [1,0,1,1,0,0] => [2,3,1] => 2
[1,1,0,0,1,0] => [1,1,0,1,0,0] => [2,1,3] => 4
[1,1,0,1,0,0] => [1,1,0,0,1,0] => [3,1,2] => 2
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [3,2,1] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 24
[1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 6
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [2,3,1,4] => 12
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 6
[1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 2
[1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => [2,1,3,4] => 18
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 4
[1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [3,1,2,4] => 12
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 4
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 2
[1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0] => [3,2,1,4] => 8
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 4
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 2
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 120
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 24
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => 48
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 24
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 72
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 12
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 48
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 12
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 6
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => 24
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 12
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 6
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 2
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 96
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 18
[1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => 36
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 18
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 4
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => 72
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 12
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => 36
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 12
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 4
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => 24
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 12
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 4
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 54
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 8
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 36
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 8
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 4
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 24
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 8
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 4
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 2
[1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => 16
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 8
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 4
[1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 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
click to show known generating functions       
Description
The number of permutations greater than or equal to the given permutation in (strong) Bruhat order.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].