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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001879
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Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 28%
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 28%
Values
[1,2] => {{1},{2}}
=> [1,2] => ([(0,1)],2)
=> ? ∊ {0,1}
[2,1] => {{1,2}}
=> [2,1] => ([],2)
=> ? ∊ {0,1}
[1,2,3] => {{1},{2},{3}}
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,3,2] => {{1},{2,3}}
=> [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,1,1,1,3}
[2,1,3] => {{1,2},{3}}
=> [2,1,3] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,1,1,3}
[2,3,1] => {{1,2,3}}
=> [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,3}
[3,1,2] => {{1,2,3}}
=> [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,3}
[3,2,1] => {{1,3},{2}}
=> [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,3}
[1,2,3,4] => {{1},{2},{3},{4}}
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,4,3] => {{1},{2},{3,4}}
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[1,3,2,4] => {{1},{2,3},{4}}
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,3,4,2] => {{1},{2,3,4}}
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[1,4,2,3] => {{1},{2,3,4}}
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[1,4,3,2] => {{1},{2,4},{3}}
=> [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[2,1,3,4] => {{1,2},{3},{4}}
=> [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[2,1,4,3] => {{1,2},{3,4}}
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[2,3,1,4] => {{1,2,3},{4}}
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[2,3,4,1] => {{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[2,4,1,3] => {{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[2,4,3,1] => {{1,2,4},{3}}
=> [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[3,1,2,4] => {{1,2,3},{4}}
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[3,1,4,2] => {{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[3,2,1,4] => {{1,3},{2},{4}}
=> [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[3,2,4,1] => {{1,3,4},{2}}
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[3,4,1,2] => {{1,3},{2,4}}
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[3,4,2,1] => {{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[4,1,2,3] => {{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[4,1,3,2] => {{1,2,4},{3}}
=> [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[4,2,1,3] => {{1,3,4},{2}}
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[4,2,3,1] => {{1,4},{2},{3}}
=> [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[4,3,1,2] => {{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[4,3,2,1] => {{1,4},{2,3}}
=> [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,6,7,7}
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,2,4,5,3] => {{1},{2},{3,4,5}}
=> [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,5,3,4] => {{1},{2},{3,4,5}}
=> [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[1,3,2,5,4] => {{1},{2,3},{4,5}}
=> [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,4,2,5] => {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[1,3,4,5,2] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,5,2,4] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,5,4,2] => {{1},{2,3,5},{4}}
=> [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,2,3,5] => {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[1,4,2,5,3] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[1,4,3,5,2] => {{1},{2,4,5},{3}}
=> [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,5,2,3] => {{1},{2,4},{3,5}}
=> [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,5,3,2] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,2,3,4] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,2,4,3] => {{1},{2,3,5},{4}}
=> [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,3,2,4] => {{1},{2,4,5},{3}}
=> [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,3,4,2] => {{1},{2,5},{3},{4}}
=> [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,4,2,3] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,4,3,2] => {{1},{2,5},{3,4}}
=> [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,3,4,5] => {{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,3,5,4] => {{1,2},{3},{4,5}}
=> [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,4,3,5] => {{1,2},{3,4},{5}}
=> [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}}
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5
[1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}}
=> [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}}
=> [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
[1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}}
=> [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
[1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}}
=> [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
[1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}}
=> [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
[1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}}
=> [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}}
=> [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
[1,3,4,5,2,6] => {{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[1,3,5,2,4,6] => {{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}}
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}}
=> [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
[1,4,2,5,3,6] => {{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}}
=> [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
[1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}}
=> [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
[1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}}
=> [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 8
[1,4,5,3,2,6] => {{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[1,5,2,3,4,6] => {{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[1,5,2,4,3,6] => {{1},{2,3,5},{4},{6}}
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[1,5,3,2,4,6] => {{1},{2,4,5},{3},{6}}
=> [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
[1,5,3,4,2,6] => {{1},{2,5},{3},{4},{6}}
=> [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[1,5,4,2,3,6] => {{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}}
=> [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}}
=> [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6
[1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}}
=> [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> 7
[1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}}
=> [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7
[1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}}
=> [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> 8
[1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}}
=> [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> 8
[1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}}
=> [1,2,3,6,5,4,7] => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> 11
[1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}}
=> [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7
[1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}}
=> [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 8
[1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}}
=> [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 9
[1,2,4,6,3,5,7] => {{1},{2},{3,4,5,6},{7}}
=> [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 9
[1,2,4,6,5,3,7] => {{1},{2},{3,4,6},{5},{7}}
=> [1,2,4,6,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
=> 11
[1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}}
=> [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 8
[1,2,5,3,6,4,7] => {{1},{2},{3,4,5,6},{7}}
=> [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 9
[1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}}
=> [1,2,5,4,3,6,7] => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> 11
[1,2,5,4,6,3,7] => {{1},{2},{3,5,6},{4},{7}}
=> [1,2,5,4,6,3,7] => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
=> 11
[1,2,5,6,3,4,7] => {{1},{2},{3,5},{4,6},{7}}
=> [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
=> 9
[1,2,5,6,4,3,7] => {{1},{2},{3,4,5,6},{7}}
=> [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 9
[1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}}
=> [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 9
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001232
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 11%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 11%
Values
[1,2] => [1,2] => [1,0,1,0]
=> [1,1,0,0]
=> 0
[2,1] => [2,1] => [1,1,0,0]
=> [1,0,1,0]
=> 1
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> 2
[2,3,1] => [3,2,1] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? ∊ {1,1,3}
[3,1,2] => [3,2,1] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? ∊ {1,1,3}
[3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? ∊ {1,1,3}
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0]
=> 3
[2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[2,3,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,3,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,4,1,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,4,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,4,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,4,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,1,2,3] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,3,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,5,5,5,5,6,7,7}
[1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,5,3,4] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 3
[1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 3
[1,3,4,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,4,5,2] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,5,2,4] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,5,4,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,2,3,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,2,5,3] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,3,5,2] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,5,2,3] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,5,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,2,3,4] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,2,4,3] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,3,2,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,3,4,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,4,2,3] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4
[2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[2,1,4,5,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,5,3,4] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,3,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,3,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,3,4,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,3,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,3,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,3,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 3
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> 3
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 4
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> 4
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 4
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 0
[1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> 2
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> 3
[1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> 3
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> 4
[1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> 4
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> 4
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> 5
[1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> 5
[1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> 5
[1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6
[2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> 6
[2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> 6
[2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> 6
[2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> 6
[2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> 6
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000454
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 11%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 11%
Values
[1,2] => [1,2] => [2] => ([],2)
=> 0
[2,1] => [2,1] => [1,1] => ([(0,1)],2)
=> 1
[1,2,3] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,3}
[1,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,3}
[2,1,3] => [2,1,3] => [1,2] => ([(1,2)],3)
=> 1
[2,3,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,3}
[3,1,2] => [3,1,2] => [1,2] => ([(1,2)],3)
=> 1
[3,2,1] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 2
[1,2,3,4] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[1,2,4,3] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[1,3,2,4] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[1,3,4,2] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[1,4,2,3] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[1,4,3,2] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,1,3,4] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,1,4,3] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,3,1,4] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,3,4,1] => [2,4,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,4,1,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[2,4,3,1] => [2,4,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,1,2,4] => [3,1,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,1,4,2] => [3,1,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,2,1,4] => [3,2,1,4] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 2
[3,2,4,1] => [3,2,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,4,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[3,4,2,1] => [3,4,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,1,2,3] => [4,1,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,1,3,2] => [4,1,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,2,1,3] => [4,2,1,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 2
[4,2,3,1] => [4,2,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,3,3,4,5,5,5,5,6,7,7}
[4,3,1,2] => [4,3,1,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 2
[4,3,2,1] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[1,2,3,4,5] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,3,5,4] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,4,3,5] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,4,5,3] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,5,3,4] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,2,5,4,3] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,2,4,5] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,2,5,4] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,4,2,5] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,4,5,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,5,2,4] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,3,5,4,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,2,3,5] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,2,5,3] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,3,2,5] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,3,5,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,5,2,3] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,4,5,3,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,2,3,4] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,2,4,3] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,3,2,4] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,3,4,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,4,2,3] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[1,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,3,4,5] => [2,1,5,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,3,5,4] => [2,1,5,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[2,1,4,3,5] => [2,1,5,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,14,14,15,15,15,15,15,15}
[4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[5,3,2,1,4] => [5,3,2,1,4] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[5,4,2,1,3] => [5,4,2,1,3] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[5,4,3,1,2] => [5,4,3,1,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[6,4,3,2,1,5] => [6,4,3,2,1,5] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[6,5,3,2,1,4] => [6,5,3,2,1,4] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[6,5,4,2,1,3] => [6,5,4,2,1,3] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[6,5,4,3,1,2] => [6,5,4,3,1,2] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(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)
=> 5
[6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2] => ([(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)
=> 5
[7,5,4,3,2,1,6] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2] => ([(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)
=> 5
[7,6,4,3,2,1,5] => [7,6,4,3,2,1,5] => [1,1,1,1,1,2] => ([(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)
=> 5
[7,6,5,3,2,1,4] => [7,6,5,3,2,1,4] => [1,1,1,1,1,2] => ([(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)
=> 5
[7,6,5,4,2,1,3] => [7,6,5,4,2,1,3] => [1,1,1,1,1,2] => ([(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)
=> 5
[7,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2] => ([(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)
=> 5
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(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)
=> 6
Description
The largest eigenvalue of a graph if it is integral.
If a graph is d-regular, then its largest eigenvalue equals d. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
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