Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001251
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
St001251: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,0,1,0]
 => [1]
 => [1]
 => 0
[1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => [1,1,1]
 => 0
[1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => [2]
 => 1
[2,1,3] => [1,1,0,0,1,0]
 => [2]
 => [1,1]
 => 0
[2,3,1] => [1,1,0,1,0,0]
 => [1]
 => [1]
 => 0
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [3,1,1,1]
 => 1
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [4,1]
 => 0
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [3,2]
 => 2
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [2,1,1]
 => 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [2,1]
 => 1
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [2,1]
 => 1
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [3,2]
 => [3,1,1]
 => 1
[2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [2,2]
 => [4]
 => 0
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [3,1]
 => [3,1]
 => 1
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,1,1]
 => 0
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [1,1]
 => [2]
 => 1
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [1,1]
 => [2]
 => 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [3]
 => [3]
 => 1
[3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [2]
 => [1,1]
 => 0
[3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [3]
 => [3]
 => 1
[3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [2]
 => [1,1]
 => 0
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [1]
 => [1]
 => 0
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [1]
 => [1]
 => 0
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [3,1,1,1,1,1,1,1]
 => 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [6,1,1,1]
 => 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [4,1,1,1,1,1]
 => 0
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [4,3,1]
 => 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [4,1,1,1]
 => 0
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [4,1,1,1]
 => 0
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [3,2,1,1,1,1]
 => 2
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [6,2]
 => 2
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [2,1,1,1,1,1,1]
 => 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [3,2,1,1]
 => 2
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [4,2]
 => 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [4,2]
 => 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [2,1,1,1,1,1]
 => 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [3,2,1]
 => 2
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [2,1,1,1,1,1]
 => 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [3,2,1]
 => 2
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [2,1,1,1]
 => 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [2,1,1,1]
 => 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [2,2]
 => 2
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [2,2]
 => 2
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [2,2]
 => 2
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [2,2]
 => 2
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [2,2]
 => 2
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [2,2]
 => 2
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [3,1,1,1,1,1,1]
 => 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [6,1,1]
 => 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [4,1,1,1,1]
 => 0
Description
The number of parts of a partition that are not congruent 1 modulo 3.