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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001232
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Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[2,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[1,1,1]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[3,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[2,2]
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[2,1,1]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[4,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[3,2]
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[3,1,1]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[2,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[5,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[4,2]
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[4,1,1]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[3,3]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[3,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[2,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,1,0,0]
=> 2
[6,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[5,2]
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[5,1,1]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[4,3]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[4,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[3,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,1,0,0]
=> 2
[2,2,2,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[7,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[6,2]
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[6,1,1]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[5,3]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[5,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[4,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,1,0,0]
=> 2
[3,3,2]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[3,2,2,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[2,2,2,2]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> 3
[8,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[7,2]
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[7,1,1]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[6,3]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[6,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[5,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,1,0,0]
=> 2
[4,3,2]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[4,2,2,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[3,3,2,1]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 3
[3,2,2,2]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> 3
[2,2,2,2,1]
=> [2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[9,1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[8,2]
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[8,1,1]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[7,3]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[7,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[6,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,1,0,0]
=> 2
[5,3,2]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001200
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 40%●distinct values known / distinct values provided: 33%
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 40%●distinct values known / distinct values provided: 33%
Values
[1,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[2,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[1,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[3,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[2,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[2,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[4,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[3,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[3,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[2,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[5,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[4,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[4,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[3,3]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 3 = 2 + 1
[3,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[2,2,2]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
[6,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[5,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[5,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[4,3]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 3 = 2 + 1
[4,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[3,2,2]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
[2,2,2,1]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
[7,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[6,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[6,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[5,3]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 3 = 2 + 1
[5,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[4,2,2]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
[3,3,2]
=> [3,2]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 2 + 1
[3,2,2,1]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
[2,2,2,2]
=> [2,2,2]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[8,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[7,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[7,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[6,3]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 3 = 2 + 1
[6,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[5,2,2]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
[4,3,2]
=> [3,2]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 2 + 1
[4,2,2,1]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
[3,3,2,1]
=> [3,2,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 3 + 1
[3,2,2,2]
=> [2,2,2]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[2,2,2,2,1]
=> [2,2,2,1]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 4 + 1
[9,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[8,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[8,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[7,3]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 3 = 2 + 1
[7,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[6,2,2]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
[5,3,2]
=> [3,2]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 2 + 1
[5,2,2,1]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
[4,3,2,1]
=> [3,2,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 3 + 1
[4,2,2,2]
=> [2,2,2]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[3,3,2,2]
=> [3,2,2]
=> [3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[3,2,2,2,1]
=> [2,2,2,1]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 4 + 1
[10,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[9,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[9,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[8,3]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 3 = 2 + 1
[8,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[7,2,2]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
[6,3,2]
=> [3,2]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 2 + 1
[6,2,2,1]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
[5,3,2,1]
=> [3,2,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 3 + 1
[5,2,2,2]
=> [2,2,2]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[4,3,2,2]
=> [3,2,2]
=> [3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[4,2,2,2,1]
=> [2,2,2,1]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 4 + 1
[3,3,2,2,1]
=> [3,2,2,1]
=> [3,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 4 + 1
[11,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[10,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[10,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[9,3]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 3 = 2 + 1
[9,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[8,2,2]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
[7,3,2]
=> [3,2]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 2 + 1
[7,2,2,1]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
[6,3,2,1]
=> [3,2,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 3 + 1
[6,2,2,2]
=> [2,2,2]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[5,3,2,2]
=> [3,2,2]
=> [3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[5,2,2,2,1]
=> [2,2,2,1]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 4 + 1
[4,3,2,2,1]
=> [3,2,2,1]
=> [3,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 4 + 1
[3,3,3,3]
=> [3,3,3]
=> [6,3]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> ? = 4 + 1
[12,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[11,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[11,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
[10,3]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 3 = 2 + 1
[10,2,1]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
[9,2,2]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
[8,3,2]
=> [3,2]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 2 + 1
[8,2,2,1]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
[7,3,2,1]
=> [3,2,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 3 + 1
[7,2,2,2]
=> [2,2,2]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[6,3,2,2]
=> [3,2,2]
=> [3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 1
[6,2,2,2,1]
=> [2,2,2,1]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 4 + 1
[5,3,2,2,1]
=> [3,2,2,1]
=> [3,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 4 + 1
[4,3,3,3]
=> [3,3,3]
=> [6,3]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> ? = 4 + 1
[3,3,3,3,1]
=> [3,3,3,1]
=> [6,3,1]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> ? = 5 + 1
[13,1]
=> [1]
=> [1]
=> [1,0]
=> ? = 0 + 1
[12,2]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> ? = 0 + 1
[12,1,1]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 2 = 1 + 1
Description
The number of simple modules in eAe with projective dimension at most 2 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA.
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