Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001291
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001291: Dyck paths ⟶ 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
[1,0,1,0,1,0]
 => [2,1]
 => [3]
 => [1,0,1,0,1,0]
 => 3
[1,0,1,1,0,0]
 => [1,1]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,0,0,1,0]
 => [2]
 => [1,1]
 => [1,1,0,0]
 => 1
[1,1,0,1,0,0]
 => [1]
 => [1]
 => [1,0]
 => 1
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 5
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 3
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 4
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [2,2]
 => [1,1,1,0,0,0]
 => 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => 5
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 3
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [3]
 => [1,0,1,0,1,0]
 => 3
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 2
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,1]
 => [1,1,0,0]
 => 1
[1,1,1,0,1,0,0,0]
 => [1]
 => [1]
 => [1,0]
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => 3
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => 5
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => 4
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => 5
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => 5
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => 2
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 3
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => 4
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => 1
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 5
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 3
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => 5
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 4
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [2,2]
 => [1,1,1,0,0,0]
 => 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 6
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => 4
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => 5
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 4
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 4
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 3
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [3]
 => [1,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 3
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,1]
 => [1,1,0,0]
 => 1
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1]
 => [1,0]
 => 1
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2,1]
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 4
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [4,2,2,1,1]
 => [3,3,2,2]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => 3
Description
The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. Let A be the Nakayama algebra associated to a Dyck path as given in [[DyckPaths/NakayamaAlgebras]]. This statistics is the number of indecomposable summands of D(A)⊗D(A), where D(A) is the natural dual of A.