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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001899
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001899: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St001899: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> [1]
=> 1
[1,0,1,0,1,0]
=> [2,1]
=> 2
[1,0,1,1,0,0]
=> [1,1]
=> 1
[1,1,0,0,1,0]
=> [2]
=> 1
[1,1,0,1,0,0]
=> [1]
=> 1
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 12
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 4
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> 4
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> 2
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> 1
[1,1,0,0,1,0,1,0]
=> [3,2]
=> 4
[1,1,0,0,1,1,0,0]
=> [2,2]
=> 2
[1,1,0,1,0,0,1,0]
=> [3,1]
=> 3
[1,1,0,1,0,1,0,0]
=> [2,1]
=> 2
[1,1,0,1,1,0,0,0]
=> [1,1]
=> 1
[1,1,1,0,0,0,1,0]
=> [3]
=> 1
[1,1,1,0,0,1,0,0]
=> [2]
=> 1
[1,1,1,0,1,0,0,0]
=> [1]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> 380
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 68
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> 84
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 33
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> 7
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> 104
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> 21
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> 46
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 18
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> 5
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> 10
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> 4
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> 104
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> 19
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> 24
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> 10
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> 3
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> 60
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> 12
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> 28
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> 12
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> 4
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> 9
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> 4
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> 18
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> 4
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> 9
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> 4
Description
The total number of irreducible representations contained in the higher Lie character for an integer partition.
Matching statistic: St001207
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 0% ●values known / values provided: 3%●distinct values known / distinct values provided: 0%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 0% ●values known / values provided: 3%●distinct values known / distinct values provided: 0%
Values
[1,0,1,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,0,1,0,1,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,0,1,1,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,0,0,1,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,0,1,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 12 + 1
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 4 + 1
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 4 + 1
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 1
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 1 + 1
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => ? = 4 + 1
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 2 + 1
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 3 + 1
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 1
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,1,0,1,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,0]
=> [6,1,2,3,4,5] => ? = 380 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => ? = 68 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => ? = 84 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 33 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ? = 7 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,0]
=> [3,1,6,2,4,5] => ? = 104 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => ? = 21 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,0]
=> [6,1,4,2,3,5] => ? = 46 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 18 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 5 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => ? = 10 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 4 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 2 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 1 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => ? = 104 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ? = 19 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => ? = 24 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => ? = 10 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => ? = 3 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => ? = 60 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => ? = 12 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => ? = 28 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 12 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 4 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => ? = 9 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 4 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 1 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => ? = 18 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => ? = 4 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => ? = 9 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => ? = 4 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 2 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => ? = 6 + 1
[1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 3 + 1
[1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 2 + 1
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 1
[1,1,1,1,0,0,1,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,1,1,0,1,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [7,1,2,3,4,5,6] => ? = 84420 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [6,1,2,3,4,7,5] => ? = 12088 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,1,2,3,7,4,6] => ? = 12872 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [7,1,2,3,6,4,5] => ? = 3784 + 1
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 1 + 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 2 + 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 1 + 1
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
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