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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001232
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(load all 3 compositions to match this statistic)
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ 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]
=> 0
{{1,2}}
=> [2] => [2] => [1,1,0,0]
=> 0
{{1},{2}}
=> [1,1] => [1,1] => [1,0,1,0]
=> 1
{{1,2,3}}
=> [3] => [3] => [1,1,1,0,0,0]
=> 0
{{1,2},{3}}
=> [2,1] => [2,1] => [1,1,0,0,1,0]
=> 1
{{1,3},{2}}
=> [2,1] => [2,1] => [1,1,0,0,1,0]
=> 1
{{1},{2,3}}
=> [1,2] => [1,2] => [1,0,1,1,0,0]
=> 2
{{1,2,3,4}}
=> [4] => [4] => [1,1,1,1,0,0,0,0]
=> 0
{{1,2,3},{4}}
=> [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
{{1,2,4},{3}}
=> [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
{{1,2},{3,4}}
=> [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
{{1,2},{3},{4}}
=> [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
{{1,3,4},{2}}
=> [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
{{1,3},{2,4}}
=> [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
{{1,3},{2},{4}}
=> [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
{{1,4},{2,3}}
=> [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
{{1},{2,3,4}}
=> [1,3] => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
{{1,4},{2},{3}}
=> [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
{{1,2,3,4,5}}
=> [5] => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 0
{{1,2,3,4},{5}}
=> [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,2,3,5},{4}}
=> [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,2,3},{4,5}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,2,3},{4},{5}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,2,4,5},{3}}
=> [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,2,4},{3,5}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,2,4},{3},{5}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,2,5},{3,4}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,2},{3,4,5}}
=> [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
{{1,2},{3,4},{5}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,2,5},{3},{4}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,2},{3,5},{4}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,3,4,5},{2}}
=> [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,3,4},{2,5}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,3,4},{2},{5}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,3,5},{2,4}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,3},{2,4,5}}
=> [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
{{1,3},{2,4},{5}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,3,5},{2},{4}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,3},{2,5},{4}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,4,5},{2,3}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,4},{2,3,5}}
=> [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
{{1,4},{2,3},{5}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,5},{2,3,4}}
=> [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
{{1},{2,3,4,5}}
=> [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4
{{1,5},{2,3},{4}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1},{2,3},{4,5}}
=> [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
{{1,4,5},{2},{3}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,4},{2,5},{3}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,5},{2,4},{3}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1},{2,4},{3,5}}
=> [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001227
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 86%
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 86%
Values
{{1}}
=> [1] => [1] => [1,0]
=> 0
{{1,2}}
=> [2] => [2] => [1,1,0,0]
=> 0
{{1},{2}}
=> [1,1] => [1,1] => [1,0,1,0]
=> 1
{{1,2,3}}
=> [3] => [3] => [1,1,1,0,0,0]
=> 0
{{1,2},{3}}
=> [2,1] => [2,1] => [1,1,0,0,1,0]
=> 1
{{1,3},{2}}
=> [2,1] => [2,1] => [1,1,0,0,1,0]
=> 1
{{1},{2,3}}
=> [1,2] => [1,2] => [1,0,1,1,0,0]
=> 2
{{1,2,3,4}}
=> [4] => [4] => [1,1,1,1,0,0,0,0]
=> 0
{{1,2,3},{4}}
=> [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
{{1,2,4},{3}}
=> [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
{{1,2},{3,4}}
=> [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
{{1,2},{3},{4}}
=> [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
{{1,3,4},{2}}
=> [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
{{1,3},{2,4}}
=> [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
{{1,3},{2},{4}}
=> [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
{{1,4},{2,3}}
=> [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
{{1},{2,3,4}}
=> [1,3] => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
{{1,4},{2},{3}}
=> [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
{{1,2,3,4,5}}
=> [5] => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 0
{{1,2,3,4},{5}}
=> [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,2,3,5},{4}}
=> [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,2,3},{4,5}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,2,3},{4},{5}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,2,4,5},{3}}
=> [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,2,4},{3,5}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,2,4},{3},{5}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,2,5},{3,4}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,2},{3,4,5}}
=> [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
{{1,2},{3,4},{5}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,2,5},{3},{4}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,2},{3,5},{4}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,3,4,5},{2}}
=> [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,3,4},{2,5}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,3,4},{2},{5}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,3,5},{2,4}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,3},{2,4,5}}
=> [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
{{1,3},{2,4},{5}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,3,5},{2},{4}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,3},{2,5},{4}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,4,5},{2,3}}
=> [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
{{1,4},{2,3,5}}
=> [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
{{1,4},{2,3},{5}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,5},{2,3,4}}
=> [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
{{1},{2,3,4,5}}
=> [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4
{{1,5},{2,3},{4}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1},{2,3},{4,5}}
=> [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
{{1,4,5},{2},{3}}
=> [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
{{1,4},{2,5},{3}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1,5},{2,4},{3}}
=> [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
{{1},{2,4},{3,5}}
=> [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
{{1,2,3,4,5,6,7}}
=> [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0
{{1,2,3,4,5,6},{7}}
=> [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
{{1,2,3,4,5,7},{6}}
=> [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
{{1,2,3,4,5},{6,7}}
=> [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
{{1,2,3,4,5},{6},{7}}
=> [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
{{1,2,3,4,6,7},{5}}
=> [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
{{1,2,3,4,6},{5,7}}
=> [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
{{1,2,3,4,6},{5},{7}}
=> [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
{{1,2,3,4,7},{5,6}}
=> [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
{{1,2,3,4},{5,6,7}}
=> [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
{{1,2,3,4},{5,6},{7}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,3,4,7},{5},{6}}
=> [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
{{1,2,3,4},{5,7},{6}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,3,4},{5},{6,7}}
=> [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
{{1,2,3,5,6,7},{4}}
=> [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
{{1,2,3,5,6},{4,7}}
=> [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
{{1,2,3,5,6},{4},{7}}
=> [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
{{1,2,3,5,7},{4,6}}
=> [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
{{1,2,3,5},{4,6,7}}
=> [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
{{1,2,3,5},{4,6},{7}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,3,5,7},{4},{6}}
=> [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
{{1,2,3,5},{4,7},{6}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,3,5},{4},{6,7}}
=> [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
{{1,2,3,6,7},{4,5}}
=> [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
{{1,2,3,6},{4,5,7}}
=> [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
{{1,2,3,6},{4,5},{7}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,3,7},{4,5,6}}
=> [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
{{1,2,3},{4,5,6,7}}
=> [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> ? = 4
{{1,2,3},{4,5,6},{7}}
=> [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> ? = 4
{{1,2,3,7},{4,5},{6}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,3},{4,5,7},{6}}
=> [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> ? = 4
{{1,2,3},{4,5},{6,7}}
=> [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
{{1,2,3},{4,5},{6},{7}}
=> [3,2,1,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
{{1,2,3,6,7},{4},{5}}
=> [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
{{1,2,3,6},{4,7},{5}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,3,6},{4},{5,7}}
=> [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
{{1,2,3,7},{4,6},{5}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,3},{4,6,7},{5}}
=> [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> ? = 4
{{1,2,3},{4,6},{5,7}}
=> [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
{{1,2,3},{4,6},{5},{7}}
=> [3,2,1,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
{{1,2,3,7},{4},{5,6}}
=> [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
{{1,2,3},{4,7},{5,6}}
=> [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
{{1,2,3},{4,7},{5},{6}}
=> [3,2,1,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
{{1,2,4,5,6,7},{3}}
=> [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
{{1,2,4,5,6},{3,7}}
=> [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
{{1,2,4,5,6},{3},{7}}
=> [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
{{1,2,4,5,7},{3,6}}
=> [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
{{1,2,4,5},{3,6,7}}
=> [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
{{1,2,4,5},{3,6},{7}}
=> [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
{{1,2,4,5,7},{3},{6}}
=> [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
Description
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
Matching statistic: St001645
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 86%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 86%
Values
{{1}}
=> [1] => [1] => ([],1)
=> 1 = 0 + 1
{{1,2}}
=> [2,1] => [1,2] => ([],2)
=> ? = 0 + 1
{{1},{2}}
=> [1,2] => [2,1] => ([(0,1)],2)
=> 2 = 1 + 1
{{1,2,3}}
=> [2,3,1] => [1,2,3] => ([],3)
=> ? = 0 + 1
{{1,2},{3}}
=> [2,1,3] => [1,3,2] => ([(1,2)],3)
=> ? = 1 + 1
{{1,3},{2}}
=> [3,2,1] => [2,1,3] => ([(1,2)],3)
=> ? = 1 + 1
{{1},{2,3}}
=> [1,3,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => ([],4)
=> ? = 0 + 1
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,4,3] => ([(2,3)],4)
=> ? = 1 + 1
{{1,2,4},{3}}
=> [2,4,3,1] => [1,3,2,4] => ([(2,3)],4)
=> ? = 1 + 1
{{1,2},{3,4}}
=> [2,1,4,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 2 + 1
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
{{1,3,4},{2}}
=> [3,2,4,1] => [2,1,3,4] => ([(2,3)],4)
=> ? = 1 + 1
{{1,3},{2,4}}
=> [3,4,1,2] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ? = 2 + 1
{{1,3},{2},{4}}
=> [3,2,1,4] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? = 3 + 1
{{1,4},{2,3}}
=> [4,3,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? = 2 + 1
{{1},{2,3,4}}
=> [1,3,4,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 + 1
{{1,4},{2},{3}}
=> [4,2,3,1] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,2,3,4,5] => ([],5)
=> ? = 0 + 1
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,5,4] => ([(3,4)],5)
=> ? = 1 + 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,4,3,5] => ([(3,4)],5)
=> ? = 1 + 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ? = 4 + 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,3,2,4,5] => ([(3,4)],5)
=> ? = 1 + 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ? = 4 + 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ? = 4 + 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [2,1,3,4,5] => ([(3,4)],5)
=> ? = 1 + 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ? = 4 + 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 + 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? = 4 + 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 1
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? = 4 + 1
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5 = 4 + 1
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 4 + 1
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([],6)
=> ? = 0 + 1
{{1,2,3,4,5},{6}}
=> [2,3,4,5,1,6] => [1,2,3,4,6,5] => ([(4,5)],6)
=> ? = 1 + 1
{{1,2,3,4,6},{5}}
=> [2,3,4,6,5,1] => [1,2,3,5,4,6] => ([(4,5)],6)
=> ? = 1 + 1
{{1,2,3,4},{5,6}}
=> [2,3,4,1,6,5] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
=> ? = 2 + 1
{{1},{2,5},{3,4,6}}
=> [1,5,4,6,2,3] => [5,6,3,2,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 6 = 5 + 1
{{1},{2,6},{3,4,5}}
=> [1,6,4,5,3,2] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
{{1},{2,4,6},{3,5,7}}
=> [1,4,5,6,7,2,3] => [6,7,2,3,4,5,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,4,7},{3,5,6}}
=> [1,4,5,7,6,3,2] => [7,6,2,3,5,4,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,4},{3,6},{5,7}}
=> [1,4,6,2,7,3,5] => [4,6,2,7,3,5,1] => ([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,4},{3,7},{5,6}}
=> [1,4,7,2,6,5,3] => [4,7,2,6,5,3,1] => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,5,6},{3,4,7}}
=> [1,5,4,7,6,2,3] => [6,7,3,2,5,4,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,5,7},{3,4,6}}
=> [1,5,4,6,7,3,2] => [7,6,3,2,4,5,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,6},{3,4,5,7}}
=> [1,6,4,5,7,2,3] => [6,7,3,4,2,5,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,7},{3,4,5,6}}
=> [1,7,4,5,6,3,2] => [7,6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,6},{3,4},{5,7}}
=> [1,6,4,3,7,2,5] => [6,4,3,7,2,5,1] => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,7},{3,4},{5,6}}
=> [1,7,4,3,6,5,2] => [7,4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,5},{3,6},{4,7}}
=> [1,5,6,7,2,3,4] => [5,6,7,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,5},{3,7},{4,6}}
=> [1,5,7,6,2,4,3] => [5,7,6,2,4,3,1] => ([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,6},{3,5},{4,7}}
=> [1,6,5,7,3,2,4] => [6,5,7,3,2,4,1] => ([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,7},{3,5},{4,6}}
=> [1,7,5,6,3,4,2] => [7,5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,6},{3,7},{4,5}}
=> [1,6,7,5,4,2,3] => [6,7,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
{{1},{2,7},{3,6},{4,5}}
=> [1,7,6,5,4,3,2] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
Description
The pebbling number of a connected graph.
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