Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001629
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2,1]
 => [1,0,1,0,1,0]
 => [1,1,1] => [3] => 1
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,1,1] => [1,2] => 0
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,2,1] => [1,1,1] => 1
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,2] => [2,1] => 0
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1] => [4] => 1
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => [1,2] => 0
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => [1,1,1] => 1
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => [2,1] => 0
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [3,1,1] => [1,2] => 0
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => [2,1] => 0
[4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,3,1] => [1,1,1] => 1
[3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => [1,1,1] => 1
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => [1,2] => 0
[3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,3] => [2,1] => 0
[5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [4,1,1] => [1,2] => 0
[5,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,4,1] => [1,1,1] => 1
[4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => [1,3] => 0
[4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,2,1,1] => [1,1,2] => 1
[4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,2,1] => [2,1,1] => 1
[3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => [3,1] => 0
[2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,4] => [2,1] => 0
[5,4,1]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => [4,1,1] => [1,2] => 0
[5,2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,4,1] => [1,1,1] => 1
[4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1] => [5] => 1
[3,2,2,2,1]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,4] => [2,1] => 0
[6,5]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,1,1] => [1,2] => 0
[6,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,5,1] => [1,1,1] => 1
[5,4,2]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [4,1,1] => [1,2] => 0
[5,4,1,1]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => [4,1,1] => [1,2] => 0
[5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [3,2,1] => [1,1,1] => 1
[5,3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,4,1] => [1,1,1] => 1
[5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [2,3,1] => [1,1,1] => 1
[5,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,4,1] => [1,1,1] => 1
[4,4,3]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [3,1,2] => [1,1,1] => 1
[4,4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,3,2] => [1,1,1] => 1
[4,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,4] => [2,1] => 0
[3,3,3,2]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3] => [1,1,1] => 1
[3,3,3,1,1]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,2,3] => [1,1,1] => 1
[3,3,2,2,1]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,4] => [2,1] => 0
[2,2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,5] => [2,1] => 0
[6,5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => [5,1,1] => [1,2] => 0
[6,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,5,1] => [1,1,1] => 1
[5,4,3]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [3,1,1,1] => [1,3] => 0
[5,4,2,1]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [4,1,1] => [1,2] => 0
[5,4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,3,1,1] => [1,1,2] => 1
[5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [3,2,1] => [1,1,1] => 1
[5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,3,1] => [1,1,1] => 1
[5,3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,4,1] => [1,1,1] => 1
[5,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,3,1] => [2,1,1] => 1
[4,4,3,1]
 => [1,1,0,1,0,0,1,0,1,1,0,0]
 => [3,1,2] => [1,1,1] => 1
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.