Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001525
Mapping
Mp00056: Parking functions —to Dyck path⟶ Dyck paths
Mp00296: Dyck paths —Knuth-Krattenthaler⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001525: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1] => [1,1,0,0]
 => [1,0,1,0]
 => [1]
 => 1
[1,1,1] => [1,1,1,0,0,0]
 => [1,1,0,0,1,0]
 => [2]
 => 0
[1,1,2] => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1]
 => 0
[1,2,1] => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1]
 => 0
[2,1,1] => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1]
 => 0
[1,1,3] => [1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [2,1]
 => 1
[1,3,1] => [1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [2,1]
 => 1
[3,1,1] => [1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [2,1]
 => 1
[1,2,2] => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => [1]
 => 1
[2,1,2] => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => [1]
 => 1
[2,2,1] => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => [1]
 => 1
[1,1,1,1] => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0]
 => [3]
 => 0
[1,1,1,2] => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2]
 => 2
[1,1,2,1] => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2]
 => 2
[1,2,1,1] => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2]
 => 2
[2,1,1,1] => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2]
 => 2
[1,1,1,3] => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [3,2]
 => 1
[1,1,3,1] => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [3,2]
 => 1
[1,3,1,1] => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [3,2]
 => 1
[3,1,1,1] => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [3,2]
 => 1
[1,1,1,4] => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [3,1]
 => 0
[1,1,4,1] => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [3,1]
 => 0
[1,4,1,1] => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [3,1]
 => 0
[4,1,1,1] => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [3,1]
 => 0
[1,1,2,2] => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 1
[1,2,1,2] => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 1
[1,2,2,1] => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 1
[2,1,1,2] => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 1
[2,1,2,1] => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 1
[2,2,1,1] => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 1
[1,1,2,3] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[1,1,3,2] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[1,2,1,3] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[1,2,3,1] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[1,3,1,2] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[1,3,2,1] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[2,1,1,3] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[2,1,3,1] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[2,3,1,1] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[3,1,1,2] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[3,1,2,1] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[3,2,1,1] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 0
[1,1,2,4] => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 0
[1,1,4,2] => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 0
[1,2,1,4] => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 0
[1,2,4,1] => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 0
[1,4,1,2] => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 0
[1,4,2,1] => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 0
[2,1,1,4] => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 0
[2,1,4,1] => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 0
Description
The number of symmetric hooks on the diagonal of a partition.