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Your data matches 19 different statistics following compositions of up to 3 maps.
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Matching statistic: St001645
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(load all 174 compositions to match this statistic)
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1] => ([],1)
=> 1
[2,1] => [2,1] => [2,1] => ([(0,1)],2)
=> 2
[3,1,2] => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[3,2,1] => [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 4
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[2,5,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[2,5,1,4,3] => [2,5,1,4,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
[2,5,4,1,3] => [2,5,4,1,3] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
[3,5,1,4,2] => [2,5,1,4,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
[3,5,2,4,1] => [2,5,1,4,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
[3,5,4,1,2] => [2,5,4,1,3] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
[4,5,1,3,2] => [2,5,1,4,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
[4,5,2,3,1] => [2,5,1,4,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
[4,5,3,1,2] => [2,5,4,1,3] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
[5,1,2,3,4] => [5,1,2,3,4] => [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
[5,1,2,4,3] => [5,1,2,4,3] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,1,3,4,2] => [5,1,2,4,3] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,1,4,2,3] => [5,1,4,2,3] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,2,3,4,1] => [5,1,2,4,3] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,3,1,2,4] => [5,3,1,2,4] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[2,6,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => ([(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
[2,6,1,3,5,4] => [2,6,1,3,5,4] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[2,6,1,4,3,5] => [2,6,1,4,3,5] => [4,6,5,3,1,2] => ([(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
[2,6,1,4,5,3] => [2,6,1,3,5,4] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[2,6,1,5,3,4] => [2,6,1,5,3,4] => [6,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[2,6,1,5,4,3] => [2,6,1,5,4,3] => [5,4,6,3,1,2] => ([(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
[2,6,4,1,3,5] => [2,6,4,1,3,5] => [6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[2,6,5,1,3,4] => [2,6,5,1,3,4] => [5,3,6,4,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 6
[2,6,5,1,4,3] => [2,6,5,1,4,3] => [6,3,5,4,1,2] => ([(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
[2,6,5,4,1,3] => [2,6,5,4,1,3] => [4,6,3,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 6
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => ([(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
[3,1,6,2,5,4] => [3,1,6,2,5,4] => [5,6,4,2,1,3] => ([(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
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [6,4,5,2,1,3] => ([(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
[3,6,1,4,2,5] => [2,6,1,4,3,5] => [4,6,5,3,1,2] => ([(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
[3,6,1,4,5,2] => [2,6,1,3,5,4] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[3,6,1,5,4,2] => [2,6,1,5,4,3] => [5,4,6,3,1,2] => ([(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
[3,6,2,1,4,5] => [3,6,2,1,4,5] => [6,5,4,1,3,2] => ([(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
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [5,6,4,1,3,2] => ([(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
[3,6,2,4,1,5] => [2,6,1,4,3,5] => [4,6,5,3,1,2] => ([(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
[3,6,2,4,5,1] => [2,6,1,3,5,4] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [6,4,5,1,3,2] => ([(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
[3,6,2,5,4,1] => [2,6,1,5,4,3] => [5,4,6,3,1,2] => ([(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
[3,6,4,1,2,5] => [2,6,4,1,3,5] => [6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[3,6,5,1,4,2] => [2,6,5,1,4,3] => [6,3,5,4,1,2] => ([(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
[3,6,5,2,4,1] => [2,6,5,1,4,3] => [6,3,5,4,1,2] => ([(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
[3,6,5,4,1,2] => [2,6,5,4,1,3] => [4,6,3,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 6
[4,1,6,2,5,3] => [3,1,6,2,5,4] => [5,6,4,2,1,3] => ([(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
[4,1,6,3,5,2] => [3,1,6,2,5,4] => [5,6,4,2,1,3] => ([(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
[4,1,6,5,2,3] => [3,1,6,5,2,4] => [6,4,5,2,1,3] => ([(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
[4,2,6,3,5,1] => [3,1,6,2,5,4] => [5,6,4,2,1,3] => ([(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
Description
The pebbling number of a connected graph.
Matching statistic: St000294
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
St000294: Binary words ⟶ ℤResult quality: 86% ●values known / values provided: 100%●distinct values known / distinct values provided: 86%
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
St000294: Binary words ⟶ ℤResult quality: 86% ●values known / values provided: 100%●distinct values known / distinct values provided: 86%
Values
[1] => [1] => [1] => => ? = 1
[2,1] => [2,1] => [1,2] => 1 => 2
[3,1,2] => [3,1,2] => [3,1,2] => 00 => 3
[3,2,1] => [3,2,1] => [1,3,2] => 10 => 4
[4,1,2,3] => [4,1,2,3] => [3,4,1,2] => 000 => 4
[2,5,1,3,4] => [2,5,1,3,4] => [4,2,5,1,3] => 0000 => 5
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[2,5,4,1,3] => [2,5,4,1,3] => [5,2,1,4,3] => 0000 => 5
[3,5,1,4,2] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[3,5,2,4,1] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[3,5,4,1,2] => [2,5,4,1,3] => [5,2,1,4,3] => 0000 => 5
[4,5,1,3,2] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[4,5,2,3,1] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[4,5,3,1,2] => [2,5,4,1,3] => [5,2,1,4,3] => 0000 => 5
[5,1,2,3,4] => [5,1,2,3,4] => [3,4,5,1,2] => 0000 => 5
[5,1,2,4,3] => [5,1,2,4,3] => [3,4,1,5,2] => 0000 => 5
[5,1,3,4,2] => [5,1,2,4,3] => [3,4,1,5,2] => 0000 => 5
[5,1,4,2,3] => [5,1,4,2,3] => [3,5,1,4,2] => 0000 => 5
[5,2,3,4,1] => [5,1,2,4,3] => [3,4,1,5,2] => 0000 => 5
[5,3,1,2,4] => [5,3,1,2,4] => [4,5,3,1,2] => 0000 => 5
[2,6,1,3,4,5] => [2,6,1,3,4,5] => [4,2,5,6,1,3] => 00000 => 6
[2,6,1,3,5,4] => [2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => 6
[2,6,1,4,3,5] => [2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => 6
[2,6,1,4,5,3] => [2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => 6
[2,6,1,5,3,4] => [2,6,1,5,3,4] => [4,2,6,1,5,3] => 00000 => 6
[2,6,1,5,4,3] => [2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => 6
[2,6,4,1,3,5] => [2,6,4,1,3,5] => [5,2,6,4,1,3] => 00000 => 6
[2,6,5,1,3,4] => [2,6,5,1,3,4] => [5,2,6,1,4,3] => 00000 => 6
[2,6,5,1,4,3] => [2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => 6
[2,6,5,4,1,3] => [2,6,5,4,1,3] => [6,2,1,5,4,3] => 00000 => 6
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [3,5,2,6,1,4] => 00000 => 6
[3,1,6,2,5,4] => [3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => 6
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [3,6,2,1,5,4] => 00000 => 6
[3,6,1,4,2,5] => [2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => 6
[3,6,1,4,5,2] => [2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => 6
[3,6,1,5,4,2] => [2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => 6
[3,6,2,1,4,5] => [3,6,2,1,4,5] => [5,4,2,6,1,3] => 00000 => 6
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [5,4,2,1,6,3] => 00000 => 6
[3,6,2,4,1,5] => [2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => 6
[3,6,2,4,5,1] => [2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => 6
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [6,4,2,1,5,3] => 00000 => 6
[3,6,2,5,4,1] => [2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => 6
[3,6,4,1,2,5] => [2,6,4,1,3,5] => [5,2,6,4,1,3] => 00000 => 6
[3,6,5,1,4,2] => [2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => 6
[3,6,5,2,4,1] => [2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => 6
[3,6,5,4,1,2] => [2,6,5,4,1,3] => [6,2,1,5,4,3] => 00000 => 6
[4,1,6,2,5,3] => [3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => 6
[4,1,6,3,5,2] => [3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => 6
[4,1,6,5,2,3] => [3,1,6,5,2,4] => [3,6,2,1,5,4] => 00000 => 6
[4,2,6,3,5,1] => [3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => 6
[4,6,1,2,3,5] => [4,6,1,2,3,5] => [4,5,6,2,1,3] => 00000 => 6
Description
The number of distinct factors of a binary word.
This is also known as the subword complexity of a binary word, see [1].
Matching statistic: St000518
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
St000518: Binary words ⟶ ℤResult quality: 86% ●values known / values provided: 100%●distinct values known / distinct values provided: 86%
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
St000518: Binary words ⟶ ℤResult quality: 86% ●values known / values provided: 100%●distinct values known / distinct values provided: 86%
Values
[1] => [1] => [1] => => ? = 1
[2,1] => [2,1] => [1,2] => 1 => 2
[3,1,2] => [3,1,2] => [3,1,2] => 00 => 3
[3,2,1] => [3,2,1] => [1,3,2] => 10 => 4
[4,1,2,3] => [4,1,2,3] => [3,4,1,2] => 000 => 4
[2,5,1,3,4] => [2,5,1,3,4] => [4,2,5,1,3] => 0000 => 5
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[2,5,4,1,3] => [2,5,4,1,3] => [5,2,1,4,3] => 0000 => 5
[3,5,1,4,2] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[3,5,2,4,1] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[3,5,4,1,2] => [2,5,4,1,3] => [5,2,1,4,3] => 0000 => 5
[4,5,1,3,2] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[4,5,2,3,1] => [2,5,1,4,3] => [4,2,1,5,3] => 0000 => 5
[4,5,3,1,2] => [2,5,4,1,3] => [5,2,1,4,3] => 0000 => 5
[5,1,2,3,4] => [5,1,2,3,4] => [3,4,5,1,2] => 0000 => 5
[5,1,2,4,3] => [5,1,2,4,3] => [3,4,1,5,2] => 0000 => 5
[5,1,3,4,2] => [5,1,2,4,3] => [3,4,1,5,2] => 0000 => 5
[5,1,4,2,3] => [5,1,4,2,3] => [3,5,1,4,2] => 0000 => 5
[5,2,3,4,1] => [5,1,2,4,3] => [3,4,1,5,2] => 0000 => 5
[5,3,1,2,4] => [5,3,1,2,4] => [4,5,3,1,2] => 0000 => 5
[2,6,1,3,4,5] => [2,6,1,3,4,5] => [4,2,5,6,1,3] => 00000 => 6
[2,6,1,3,5,4] => [2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => 6
[2,6,1,4,3,5] => [2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => 6
[2,6,1,4,5,3] => [2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => 6
[2,6,1,5,3,4] => [2,6,1,5,3,4] => [4,2,6,1,5,3] => 00000 => 6
[2,6,1,5,4,3] => [2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => 6
[2,6,4,1,3,5] => [2,6,4,1,3,5] => [5,2,6,4,1,3] => 00000 => 6
[2,6,5,1,3,4] => [2,6,5,1,3,4] => [5,2,6,1,4,3] => 00000 => 6
[2,6,5,1,4,3] => [2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => 6
[2,6,5,4,1,3] => [2,6,5,4,1,3] => [6,2,1,5,4,3] => 00000 => 6
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [3,5,2,6,1,4] => 00000 => 6
[3,1,6,2,5,4] => [3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => 6
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [3,6,2,1,5,4] => 00000 => 6
[3,6,1,4,2,5] => [2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => 6
[3,6,1,4,5,2] => [2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => 6
[3,6,1,5,4,2] => [2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => 6
[3,6,2,1,4,5] => [3,6,2,1,4,5] => [5,4,2,6,1,3] => 00000 => 6
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [5,4,2,1,6,3] => 00000 => 6
[3,6,2,4,1,5] => [2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => 6
[3,6,2,4,5,1] => [2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => 6
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [6,4,2,1,5,3] => 00000 => 6
[3,6,2,5,4,1] => [2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => 6
[3,6,4,1,2,5] => [2,6,4,1,3,5] => [5,2,6,4,1,3] => 00000 => 6
[3,6,5,1,4,2] => [2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => 6
[3,6,5,2,4,1] => [2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => 6
[3,6,5,4,1,2] => [2,6,5,4,1,3] => [6,2,1,5,4,3] => 00000 => 6
[4,1,6,2,5,3] => [3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => 6
[4,1,6,3,5,2] => [3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => 6
[4,1,6,5,2,3] => [3,1,6,5,2,4] => [3,6,2,1,5,4] => 00000 => 6
[4,2,6,3,5,1] => [3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => 6
[4,6,1,2,3,5] => [4,6,1,2,3,5] => [4,5,6,2,1,3] => 00000 => 6
Description
The number of distinct subsequences in a binary word.
In contrast to the subword complexity [[St000294]] this is the cardinality of the set of all subsequences of not necessarily consecutive letters.
Matching statistic: St000829
(load all 26 compositions to match this statistic)
(load all 26 compositions to match this statistic)
Mp00252: Permutations —restriction⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St000829: Permutations ⟶ ℤResult quality: 71% ●values known / values provided: 100%●distinct values known / distinct values provided: 71%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St000829: Permutations ⟶ ℤResult quality: 71% ●values known / values provided: 100%●distinct values known / distinct values provided: 71%
Values
[1] => [] => [] => ? = 1 - 3
[2,1] => [1] => [1] => ? = 2 - 3
[3,1,2] => [1,2] => [1,2] => 0 = 3 - 3
[3,2,1] => [2,1] => [2,1] => 1 = 4 - 3
[4,1,2,3] => [1,2,3] => [1,3,2] => 1 = 4 - 3
[2,5,1,3,4] => [2,1,3,4] => [2,1,4,3] => 2 = 5 - 3
[2,5,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2 = 5 - 3
[2,5,4,1,3] => [2,4,1,3] => [2,4,1,3] => 2 = 5 - 3
[3,5,1,4,2] => [3,1,4,2] => [3,1,4,2] => 2 = 5 - 3
[3,5,2,4,1] => [3,2,4,1] => [3,2,4,1] => 2 = 5 - 3
[3,5,4,1,2] => [3,4,1,2] => [3,4,1,2] => 2 = 5 - 3
[4,5,1,3,2] => [4,1,3,2] => [4,1,3,2] => 2 = 5 - 3
[4,5,2,3,1] => [4,2,3,1] => [4,2,3,1] => 2 = 5 - 3
[4,5,3,1,2] => [4,3,1,2] => [4,3,1,2] => 2 = 5 - 3
[5,1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 2 = 5 - 3
[5,1,2,4,3] => [1,2,4,3] => [1,4,3,2] => 2 = 5 - 3
[5,1,3,4,2] => [1,3,4,2] => [1,4,3,2] => 2 = 5 - 3
[5,1,4,2,3] => [1,4,2,3] => [1,4,3,2] => 2 = 5 - 3
[5,2,3,4,1] => [2,3,4,1] => [2,4,3,1] => 2 = 5 - 3
[5,3,1,2,4] => [3,1,2,4] => [3,1,4,2] => 2 = 5 - 3
[2,6,1,3,4,5] => [2,1,3,4,5] => [2,1,5,4,3] => 3 = 6 - 3
[2,6,1,3,5,4] => [2,1,3,5,4] => [2,1,5,4,3] => 3 = 6 - 3
[2,6,1,4,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 3 = 6 - 3
[2,6,1,4,5,3] => [2,1,4,5,3] => [2,1,5,4,3] => 3 = 6 - 3
[2,6,1,5,3,4] => [2,1,5,3,4] => [2,1,5,4,3] => 3 = 6 - 3
[2,6,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 3 = 6 - 3
[2,6,4,1,3,5] => [2,4,1,3,5] => [2,5,1,4,3] => 3 = 6 - 3
[2,6,5,1,3,4] => [2,5,1,3,4] => [2,5,1,4,3] => 3 = 6 - 3
[2,6,5,1,4,3] => [2,5,1,4,3] => [2,5,1,4,3] => 3 = 6 - 3
[2,6,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => 3 = 6 - 3
[3,1,6,2,4,5] => [3,1,2,4,5] => [3,1,5,4,2] => 3 = 6 - 3
[3,1,6,2,5,4] => [3,1,2,5,4] => [3,1,5,4,2] => 3 = 6 - 3
[3,1,6,5,2,4] => [3,1,5,2,4] => [3,1,5,4,2] => 3 = 6 - 3
[3,6,1,4,2,5] => [3,1,4,2,5] => [3,1,5,4,2] => 3 = 6 - 3
[3,6,1,4,5,2] => [3,1,4,5,2] => [3,1,5,4,2] => 3 = 6 - 3
[3,6,1,5,4,2] => [3,1,5,4,2] => [3,1,5,4,2] => 3 = 6 - 3
[3,6,2,1,4,5] => [3,2,1,4,5] => [3,2,1,5,4] => 3 = 6 - 3
[3,6,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 3 = 6 - 3
[3,6,2,4,1,5] => [3,2,4,1,5] => [3,2,5,1,4] => 3 = 6 - 3
[3,6,2,4,5,1] => [3,2,4,5,1] => [3,2,5,4,1] => 3 = 6 - 3
[3,6,2,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => 3 = 6 - 3
[3,6,2,5,4,1] => [3,2,5,4,1] => [3,2,5,4,1] => 3 = 6 - 3
[3,6,4,1,2,5] => [3,4,1,2,5] => [3,5,1,4,2] => 3 = 6 - 3
[3,6,5,1,4,2] => [3,5,1,4,2] => [3,5,1,4,2] => 3 = 6 - 3
[3,6,5,2,4,1] => [3,5,2,4,1] => [3,5,2,4,1] => 3 = 6 - 3
[3,6,5,4,1,2] => [3,5,4,1,2] => [3,5,4,1,2] => 3 = 6 - 3
[4,1,6,2,5,3] => [4,1,2,5,3] => [4,1,5,3,2] => 3 = 6 - 3
[4,1,6,3,5,2] => [4,1,3,5,2] => [4,1,5,3,2] => 3 = 6 - 3
[4,1,6,5,2,3] => [4,1,5,2,3] => [4,1,5,3,2] => 3 = 6 - 3
[4,2,6,3,5,1] => [4,2,3,5,1] => [4,2,5,3,1] => 3 = 6 - 3
[4,6,1,2,3,5] => [4,1,2,3,5] => [4,1,5,3,2] => 3 = 6 - 3
[4,6,1,5,3,2] => [4,1,5,3,2] => [4,1,5,3,2] => 3 = 6 - 3
Description
The Ulam distance of a permutation to the identity permutation.
This is, for a permutation $\pi$ of $n$, given by $n$ minus the length of the longest increasing subsequence of $\pi^{-1}$.
In other words, this statistic plus [[St000062]] equals $n$.
Matching statistic: St001570
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001570: Graphs ⟶ ℤResult quality: 57% ●values known / values provided: 100%●distinct values known / distinct values provided: 57%
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001570: Graphs ⟶ ℤResult quality: 57% ●values known / values provided: 100%●distinct values known / distinct values provided: 57%
Values
[1] => => [] => ?
=> ? = 1 - 1
[2,1] => 0 => [1] => ([],1)
=> ? = 2 - 1
[3,1,2] => 00 => [2] => ([],2)
=> ? = 3 - 1
[3,2,1] => 00 => [2] => ([],2)
=> ? = 4 - 1
[4,1,2,3] => 000 => [3] => ([],3)
=> 3 = 4 - 1
[2,5,1,3,4] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[2,5,1,4,3] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[2,5,4,1,3] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[3,5,1,4,2] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[3,5,2,4,1] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[3,5,4,1,2] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[4,5,1,3,2] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[4,5,2,3,1] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[4,5,3,1,2] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[5,1,2,3,4] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[5,1,2,4,3] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[5,1,3,4,2] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[5,1,4,2,3] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[5,2,3,4,1] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[5,3,1,2,4] => 0000 => [4] => ([],4)
=> 4 = 5 - 1
[2,6,1,3,4,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,1,3,5,4] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,1,4,3,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,1,4,5,3] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,1,5,3,4] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,1,5,4,3] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,4,1,3,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,5,1,3,4] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,5,1,4,3] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[2,6,5,4,1,3] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,1,6,2,4,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,1,6,2,5,4] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,1,6,5,2,4] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,1,4,2,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,1,4,5,2] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,1,5,4,2] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,2,1,4,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,2,1,5,4] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,2,4,1,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,2,4,5,1] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,2,5,1,4] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,2,5,4,1] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,4,1,2,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,5,1,4,2] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,5,2,4,1] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[3,6,5,4,1,2] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[4,1,6,2,5,3] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[4,1,6,3,5,2] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[4,1,6,5,2,3] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[4,2,6,3,5,1] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[4,6,1,2,3,5] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[4,6,1,5,3,2] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[4,6,2,1,5,3] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
[4,6,2,5,1,3] => 00000 => [5] => ([],5)
=> 5 = 6 - 1
Description
The minimal number of edges to add to make a graph Hamiltonian.
A graph is Hamiltonian if it contains a cycle as a subgraph, which contains all vertices.
Matching statistic: St001880
(load all 12 compositions to match this statistic)
(load all 12 compositions to match this statistic)
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St001880: Posets ⟶ ℤResult quality: 71% ●values known / values provided: 82%●distinct values known / distinct values provided: 71%
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St001880: Posets ⟶ ℤResult quality: 71% ●values known / values provided: 82%●distinct values known / distinct values provided: 71%
Values
[1] => [1] => => ?
=> ? = 1
[2,1] => [1,2] => 1 => ([(0,1)],2)
=> ? = 2
[3,1,2] => [3,1,2] => 00 => ([(0,2),(2,1)],3)
=> 3
[3,2,1] => [1,3,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,1,2,3] => [3,4,1,2] => 000 => ([(0,3),(2,1),(3,2)],4)
=> 4
[2,5,1,3,4] => [4,2,5,1,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,5,1,4,3] => [4,2,1,5,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,5,4,1,3] => [5,2,1,4,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,5,1,4,2] => [4,1,2,5,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,5,2,4,1] => [1,4,2,5,3] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[3,5,4,1,2] => [5,1,2,4,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,1,3,2] => [4,1,5,2,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,2,3,1] => [1,4,5,2,3] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[4,5,3,1,2] => [5,1,4,2,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,2,3,4] => [3,4,5,1,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,2,4,3] => [3,4,1,5,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,3,4,2] => [3,1,4,5,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,4,2,3] => [3,5,1,4,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,3,4,1] => [1,3,4,5,2] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[5,3,1,2,4] => [4,5,3,1,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,6,1,3,4,5] => [4,2,5,6,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,4,5,3] => [4,2,1,5,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,5,3,4] => [4,2,6,1,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,4,1,3,5] => [5,2,6,4,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,1,3,4] => [5,2,6,1,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,4,1,3] => [6,2,1,5,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,2,4,5] => [3,5,2,6,1,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,5,2,4] => [3,6,2,1,5,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,4,2,5] => [4,6,2,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,4,5,2] => [4,1,2,5,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,5,4,2] => [4,1,2,6,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,1,4,5] => [5,4,2,6,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,1,5,4] => [5,4,2,1,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,4,1,5] => [6,4,2,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,4,5,1] => [1,4,2,5,6,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,2,5,1,4] => [6,4,2,1,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,5,4,1] => [1,4,2,6,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,4,1,2,5] => [5,6,2,4,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,5,1,4,2] => [5,1,2,6,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,5,2,4,1] => [1,5,2,6,4,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,5,4,1,2] => [6,1,2,5,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,2,5,3] => [3,5,1,2,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,3,5,2] => [3,1,5,2,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,5,2,3] => [3,6,1,2,5,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,2,6,3,5,1] => [1,3,5,2,6,4] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,1,2,3,5] => [4,5,6,2,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,1,5,3,2] => [4,1,6,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,1,5,3] => [5,4,1,2,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,5,1,3] => [6,4,1,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,5,3,1] => [1,4,6,2,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,3,1,5,2] => [5,1,4,2,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,3,2,5,1] => [1,5,4,2,6,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,3,5,1,2] => [6,1,4,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,3,5,2,1] => [1,6,4,2,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,1,3,2] => [5,1,6,2,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,5,2,3,1] => [1,5,6,2,4,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,3,1,2] => [6,1,5,2,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,1,6,2,4,3] => [3,5,1,6,2,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,2,6,3,4,1] => [1,3,5,6,2,4] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,2,4,3,1] => [1,4,6,5,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,3,2,4,1] => [1,5,4,6,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,3,4,2,1] => [1,6,4,5,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,4,2,3,1] => [1,5,6,4,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,3,4,5,1] => [1,3,4,5,6,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,3,5,4,1] => [1,3,4,6,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,4,5,3,1] => [1,3,6,4,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,5,3,4,1] => [1,3,5,6,4,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,3,4,5,2,1] => [1,6,3,4,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,4,2,3,5,1] => [1,4,5,3,6,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,5,2,4,3,1] => [1,4,6,5,3,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,5,3,4,2,1] => [1,6,4,5,3,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,5,2,7,4,6,1] => [1,4,2,6,3,7,5] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,6,2,7,4,5,1] => [1,4,2,6,7,3,5] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,2,4,5,6,1] => [1,4,2,5,6,7,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,2,4,6,5,1] => [1,4,2,5,7,6,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,2,5,4,6,1] => [1,4,2,6,5,7,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,2,5,6,4,1] => [1,4,2,7,5,6,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,2,6,4,5,1] => [1,4,2,6,7,5,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,2,6,5,4,1] => [1,4,2,7,6,5,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,5,2,4,6,1] => [1,5,2,6,4,7,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,6,2,4,5,1] => [1,5,2,6,7,4,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,6,2,5,4,1] => [1,5,2,7,6,4,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[3,7,6,5,2,4,1] => [1,6,2,7,5,4,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,2,7,3,5,6,1] => [1,3,5,2,6,7,4] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,2,7,3,6,5,1] => [1,3,5,2,7,6,4] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,2,7,6,3,5,1] => [1,3,6,2,7,5,4] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,5,2,7,3,6,1] => [1,4,6,2,3,7,5] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,6,2,7,3,5,1] => [1,4,6,2,7,3,5] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,7,2,5,3,6,1] => [1,4,6,2,5,7,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,7,2,5,6,3,1] => [1,4,7,2,5,6,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,7,2,6,5,3,1] => [1,4,7,2,6,5,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,7,3,2,5,6,1] => [1,5,4,2,6,7,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,7,3,2,6,5,1] => [1,5,4,2,7,6,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,7,3,5,2,6,1] => [1,6,4,2,5,7,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
[4,7,3,5,6,2,1] => [1,7,4,2,5,6,3] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? = 7
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000454
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 86%
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 86%
Values
[1] => ([],1)
=> [1] => ([],1)
=> 0 = 1 - 1
[2,1] => ([(0,1)],2)
=> [1,1] => ([(0,1)],2)
=> 1 = 2 - 1
[3,1,2] => ([(0,2),(1,2)],3)
=> [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> [2,1] => ([(0,2),(1,2)],3)
=> ? = 4 - 1
[4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> [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 - 1
[2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [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 - 1
[2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [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 - 1
[3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [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 - 1
[3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [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 - 1
[3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [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 - 1
[4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [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 - 1
[4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [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 - 1
[5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [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 - 1
[5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [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 - 1
[2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[2,6,1,3,5,4] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [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 - 1
[2,6,1,4,3,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [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 - 1
[2,6,1,4,5,3] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [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 - 1
[2,6,1,5,3,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [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 - 1
[2,6,1,5,4,3] => ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[2,6,4,1,3,5] => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[2,6,5,1,3,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[2,6,5,1,4,3] => ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [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 - 1
[3,1,6,2,5,4] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,1,4,2,5] => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,1,4,5,2] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,1,5,4,2] => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,2,1,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,2,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[3,6,2,4,1,5] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,2,4,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,2,5,1,4] => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,2,5,4,1] => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,4,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [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 - 1
[3,6,5,1,4,2] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,5,2,4,1] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[3,6,5,4,1,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[4,1,6,2,5,3] => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [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 - 1
[4,1,6,3,5,2] => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [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 - 1
[4,1,6,5,2,3] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[4,2,6,3,5,1] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [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 - 1
[4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[4,6,1,5,3,2] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[4,6,2,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[4,6,2,5,1,3] => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[4,6,2,5,3,1] => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[4,6,3,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[4,6,3,2,5,1] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[4,6,3,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[4,6,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,1,1,1,1] => ([(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 - 1
[4,6,5,1,3,2] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[4,6,5,2,3,1] => ([(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)
=> [2,1,1,1,1] => ([(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 - 1
[4,6,5,3,1,2] => ([(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)
=> [2,1,1,1,1] => ([(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 - 1
[5,1,6,2,4,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [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 - 1
[5,1,6,3,4,2] => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[5,1,6,4,2,3] => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[5,2,6,3,4,1] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,6,1,4,3,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[5,6,2,1,4,3] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,6,2,4,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[5,6,2,4,3,1] => ([(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)
=> [2,1,1,1,1] => ([(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 - 1
[5,6,3,1,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[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)
=> [2,1,1,1,1] => ([(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 - 1
[5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,6,4,1,3,2] => ([(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)
=> [2,1,1,1,1] => ([(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 - 1
[5,6,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,2,3,5,4] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,2,4,3,5] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,2,4,5,3] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,2,5,3,4] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,2,5,4,3] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,3,4,2,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,3,4,5,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[6,1,3,5,4,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[6,1,4,2,3,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,1,4,5,3,2] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[6,1,5,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[6,1,5,2,4,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[6,1,5,3,2,4] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[6,1,5,3,4,2] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[6,1,5,4,2,3] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,1,1,1] => ([(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 - 1
[6,2,3,4,1,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => ([(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 - 1
[6,2,3,4,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,2,3,5,4,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,2,4,5,3,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,1,1,1,1] => ([(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 - 1
[6,2,5,3,1,4] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
[6,3,1,2,5,4] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [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 - 1
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.
Matching statistic: St001232
(load all 16 compositions to match this statistic)
(load all 16 compositions to match this statistic)
Mp00223: Permutations —runsort⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 45% ●values known / values provided: 45%●distinct values known / distinct values provided: 71%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 45% ●values known / values provided: 45%●distinct values known / distinct values provided: 71%
Values
[1] => [1] => [1,0]
=> [1,0]
=> 0 = 1 - 1
[2,1] => [1,2] => [1,0,1,0]
=> [1,0,1,0]
=> 1 = 2 - 1
[3,1,2] => [1,2,3] => [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> ? = 3 - 1
[3,2,1] => [1,2,3] => [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> ? = 4 - 1
[4,1,2,3] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 4 - 1
[2,5,1,3,4] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? = 5 - 1
[2,5,1,4,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4 = 5 - 1
[2,5,4,1,3] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4 = 5 - 1
[3,5,1,4,2] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4 = 5 - 1
[3,5,2,4,1] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? = 5 - 1
[3,5,4,1,2] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ? = 5 - 1
[4,5,1,3,2] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 5 - 1
[4,5,2,3,1] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 5 - 1
[4,5,3,1,2] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 5 - 1
[5,1,2,3,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 5 - 1
[5,1,2,4,3] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? = 5 - 1
[5,1,3,4,2] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? = 5 - 1
[5,1,4,2,3] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4 = 5 - 1
[5,2,3,4,1] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 5 - 1
[5,3,1,2,4] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? = 5 - 1
[2,6,1,3,4,5] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
[2,6,1,3,5,4] => [1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? = 6 - 1
[2,6,1,4,3,5] => [1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
[2,6,1,4,5,3] => [1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5 = 6 - 1
[2,6,1,5,3,4] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
[2,6,1,5,4,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
[2,6,4,1,3,5] => [1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? = 6 - 1
[2,6,5,1,3,4] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? = 6 - 1
[2,6,5,1,4,3] => [1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
[2,6,5,4,1,3] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
[3,1,6,2,4,5] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[3,1,6,2,5,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[3,1,6,5,2,4] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[3,6,1,4,2,5] => [1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
[3,6,1,4,5,2] => [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? = 6 - 1
[3,6,1,5,4,2] => [1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5 = 6 - 1
[3,6,2,1,4,5] => [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? = 6 - 1
[3,6,2,1,5,4] => [1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5 = 6 - 1
[3,6,2,4,1,5] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[3,6,2,4,5,1] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? = 6 - 1
[3,6,2,5,1,4] => [1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
[3,6,2,5,4,1] => [1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? = 6 - 1
[3,6,4,1,2,5] => [1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? = 6 - 1
[3,6,5,1,4,2] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5 = 6 - 1
[3,6,5,2,4,1] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? = 6 - 1
[3,6,5,4,1,2] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 6 - 1
[4,1,6,2,5,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[4,1,6,3,5,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[4,1,6,5,2,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[4,2,6,3,5,1] => [1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 6 - 1
[4,6,1,2,3,5] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? = 6 - 1
[4,6,1,5,3,2] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[4,6,2,1,5,3] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[4,6,2,5,1,3] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
[4,6,2,5,3,1] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? = 6 - 1
[4,6,3,1,5,2] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[4,6,3,2,5,1] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? = 6 - 1
[4,6,3,5,1,2] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? = 6 - 1
[4,6,3,5,2,1] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? = 6 - 1
[4,6,5,1,3,2] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> ? = 6 - 1
[4,6,5,2,3,1] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 6 - 1
[4,6,5,3,1,2] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 6 - 1
[5,1,6,2,4,3] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[5,1,6,3,4,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[5,1,6,4,2,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[5,2,6,3,4,1] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 6 - 1
[5,6,1,2,3,4] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 6 - 1
[5,6,1,4,3,2] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 6 - 1
[5,6,2,1,4,3] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 6 - 1
[5,6,2,4,1,3] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ? = 6 - 1
[5,6,2,4,3,1] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? = 6 - 1
[5,6,3,1,4,2] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 6 - 1
[5,6,3,2,4,1] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? = 6 - 1
[5,6,3,4,1,2] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 6 - 1
[5,6,3,4,2,1] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 6 - 1
[5,6,4,1,3,2] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ? = 6 - 1
[5,6,4,2,3,1] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 6 - 1
[5,6,4,3,1,2] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 6 - 1
[6,1,2,3,4,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 6 - 1
[6,1,2,3,5,4] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? = 6 - 1
[6,1,2,4,3,5] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? = 6 - 1
[6,1,2,4,5,3] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? = 6 - 1
[6,1,3,4,5,2] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
[6,1,5,2,3,4] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[6,1,5,2,4,3] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[6,1,5,3,2,4] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[6,1,5,3,4,2] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[6,1,5,4,2,3] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[6,2,3,4,1,5] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[6,2,5,3,1,4] => [1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
[6,3,1,5,2,4] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[6,4,1,3,2,5] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
[6,4,1,5,2,3] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[6,4,2,3,1,5] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[2,4,1,7,3,5,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[2,4,1,7,3,6,5] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[2,4,1,7,6,3,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[2,5,1,7,3,6,4] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[2,5,1,7,4,6,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[2,5,1,7,6,3,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000189
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000189: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 71%
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000189: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 71%
Values
[1] => [1] => => ?
=> ? = 1
[2,1] => [1,2] => 1 => ([(0,1)],2)
=> 2
[3,1,2] => [3,1,2] => 00 => ([(0,2),(2,1)],3)
=> 3
[3,2,1] => [1,3,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,1,2,3] => [3,4,1,2] => 000 => ([(0,3),(2,1),(3,2)],4)
=> 4
[2,5,1,3,4] => [4,2,5,1,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,5,1,4,3] => [4,2,1,5,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,5,4,1,3] => [5,2,1,4,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,5,1,4,2] => [4,1,2,5,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,5,2,4,1] => [1,4,2,5,3] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[3,5,4,1,2] => [5,1,2,4,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,1,3,2] => [4,1,5,2,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,2,3,1] => [1,4,5,2,3] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[4,5,3,1,2] => [5,1,4,2,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,2,3,4] => [3,4,5,1,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,2,4,3] => [3,4,1,5,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,3,4,2] => [3,1,4,5,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,4,2,3] => [3,5,1,4,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,3,4,1] => [1,3,4,5,2] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[5,3,1,2,4] => [4,5,3,1,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,6,1,3,4,5] => [4,2,5,6,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,4,5,3] => [4,2,1,5,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,5,3,4] => [4,2,6,1,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,4,1,3,5] => [5,2,6,4,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,1,3,4] => [5,2,6,1,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,4,1,3] => [6,2,1,5,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,2,4,5] => [3,5,2,6,1,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,5,2,4] => [3,6,2,1,5,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,4,2,5] => [4,6,2,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,4,5,2] => [4,1,2,5,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,5,4,2] => [4,1,2,6,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,1,4,5] => [5,4,2,6,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,1,5,4] => [5,4,2,1,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,4,1,5] => [6,4,2,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,4,5,1] => [1,4,2,5,6,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,2,5,1,4] => [6,4,2,1,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,5,4,1] => [1,4,2,6,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,4,1,2,5] => [5,6,2,4,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,5,1,4,2] => [5,1,2,6,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,5,2,4,1] => [1,5,2,6,4,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,5,4,1,2] => [6,1,2,5,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,2,5,3] => [3,5,1,2,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,3,5,2] => [3,1,5,2,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,5,2,3] => [3,6,1,2,5,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,2,6,3,5,1] => [1,3,5,2,6,4] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,1,2,3,5] => [4,5,6,2,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,1,5,3,2] => [4,1,6,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,1,5,3] => [5,4,1,2,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,5,1,3] => [6,4,1,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,5,3,1] => [1,4,6,2,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,3,1,5,2] => [5,1,4,2,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,3,2,5,1] => [1,5,4,2,6,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,3,5,1,2] => [6,1,4,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,3,5,2,1] => [1,6,4,2,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,1,3,2] => [5,1,6,2,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,5,2,3,1] => [1,5,6,2,4,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,3,1,2] => [6,1,5,2,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,2,6,3,4,1] => [1,3,5,6,2,4] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,2,4,3,1] => [1,4,6,5,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,3,2,4,1] => [1,5,4,6,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,3,4,2,1] => [1,6,4,5,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,4,2,3,1] => [1,5,6,4,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,3,4,5,1] => [1,3,4,5,6,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,3,5,4,1] => [1,3,4,6,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,4,5,3,1] => [1,3,6,4,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,5,3,4,1] => [1,3,5,6,4,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,3,4,5,2,1] => [1,6,3,4,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,4,2,3,5,1] => [1,4,5,3,6,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,5,2,4,3,1] => [1,4,6,5,3,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,5,3,4,2,1] => [1,6,4,5,3,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[2,4,1,7,3,5,6] => [4,2,6,3,7,1,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,4,1,7,3,6,5] => [4,2,6,3,1,7,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,4,1,7,6,3,5] => [4,2,7,3,1,6,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,5,1,7,3,6,4] => [4,2,6,1,3,7,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,5,1,7,4,6,3] => [4,2,1,6,3,7,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,5,1,7,6,3,4] => [4,2,7,1,3,6,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,5,7,1,3,4,6] => [5,2,6,7,3,1,4] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,6,1,7,3,5,4] => [4,2,6,1,7,3,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,6,1,7,4,5,3] => [4,2,1,6,7,3,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,6,1,7,5,3,4] => [4,2,7,1,6,3,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,6,7,1,3,4,5] => [5,2,6,7,1,3,4] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,4,5,6] => [4,2,5,6,7,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,4,6,5] => [4,2,5,6,1,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,5,4,6] => [4,2,5,7,6,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,5,6,4] => [4,2,5,1,6,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,6,4,5] => [4,2,5,7,1,6,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,6,5,4] => [4,2,5,1,7,6,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,3,5,6] => [4,2,6,5,7,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,3,6,5] => [4,2,6,5,1,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,5,3,6] => [4,2,7,5,6,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,5,6,3] => [4,2,1,5,6,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,6,3,5] => [4,2,7,5,1,6,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,6,5,3] => [4,2,1,5,7,6,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,5,3,4,6] => [4,2,6,7,5,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,5,3,6,4] => [4,2,6,1,5,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
Description
The number of elements in the poset.
Matching statistic: St000656
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000656: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 71%
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000656: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 71%
Values
[1] => [1] => => ?
=> ? = 1
[2,1] => [1,2] => 1 => ([(0,1)],2)
=> 2
[3,1,2] => [3,1,2] => 00 => ([(0,2),(2,1)],3)
=> 3
[3,2,1] => [1,3,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,1,2,3] => [3,4,1,2] => 000 => ([(0,3),(2,1),(3,2)],4)
=> 4
[2,5,1,3,4] => [4,2,5,1,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,5,1,4,3] => [4,2,1,5,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,5,4,1,3] => [5,2,1,4,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,5,1,4,2] => [4,1,2,5,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,5,2,4,1] => [1,4,2,5,3] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[3,5,4,1,2] => [5,1,2,4,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,1,3,2] => [4,1,5,2,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,2,3,1] => [1,4,5,2,3] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[4,5,3,1,2] => [5,1,4,2,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,2,3,4] => [3,4,5,1,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,2,4,3] => [3,4,1,5,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,3,4,2] => [3,1,4,5,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,1,4,2,3] => [3,5,1,4,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,3,4,1] => [1,3,4,5,2] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[5,3,1,2,4] => [4,5,3,1,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[2,6,1,3,4,5] => [4,2,5,6,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,3,5,4] => [4,2,5,1,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,4,3,5] => [4,2,6,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,4,5,3] => [4,2,1,5,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,5,3,4] => [4,2,6,1,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,1,5,4,3] => [4,2,1,6,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,4,1,3,5] => [5,2,6,4,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,1,3,4] => [5,2,6,1,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,1,4,3] => [5,2,1,6,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,6,5,4,1,3] => [6,2,1,5,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,2,4,5] => [3,5,2,6,1,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,2,5,4] => [3,5,2,1,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,1,6,5,2,4] => [3,6,2,1,5,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,4,2,5] => [4,6,2,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,4,5,2] => [4,1,2,5,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,1,5,4,2] => [4,1,2,6,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,1,4,5] => [5,4,2,6,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,1,5,4] => [5,4,2,1,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,4,1,5] => [6,4,2,5,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,4,5,1] => [1,4,2,5,6,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,2,5,1,4] => [6,4,2,1,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,2,5,4,1] => [1,4,2,6,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,4,1,2,5] => [5,6,2,4,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,5,1,4,2] => [5,1,2,6,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,6,5,2,4,1] => [1,5,2,6,4,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[3,6,5,4,1,2] => [6,1,2,5,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,2,5,3] => [3,5,1,2,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,3,5,2] => [3,1,5,2,6,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,1,6,5,2,3] => [3,6,1,2,5,4] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,2,6,3,5,1] => [1,3,5,2,6,4] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,1,2,3,5] => [4,5,6,2,1,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,1,5,3,2] => [4,1,6,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,1,5,3] => [5,4,1,2,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,5,1,3] => [6,4,1,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,2,5,3,1] => [1,4,6,2,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,3,1,5,2] => [5,1,4,2,6,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,3,2,5,1] => [1,5,4,2,6,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,3,5,1,2] => [6,1,4,2,5,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,3,5,2,1] => [1,6,4,2,5,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,1,3,2] => [5,1,6,2,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,6,5,2,3,1] => [1,5,6,2,4,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,3,1,2] => [6,1,5,2,4,3] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,2,6,3,4,1] => [1,3,5,6,2,4] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,2,4,3,1] => [1,4,6,5,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,3,2,4,1] => [1,5,4,6,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,3,4,2,1] => [1,6,4,5,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,4,2,3,1] => [1,5,6,4,2,3] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,3,4,5,1] => [1,3,4,5,6,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,3,5,4,1] => [1,3,4,6,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,4,5,3,1] => [1,3,6,4,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,2,5,3,4,1] => [1,3,5,6,4,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,3,4,5,2,1] => [1,6,3,4,5,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,4,2,3,5,1] => [1,4,5,3,6,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,5,2,4,3,1] => [1,4,6,5,3,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[6,5,3,4,2,1] => [1,6,4,5,3,2] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[2,4,1,7,3,5,6] => [4,2,6,3,7,1,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,4,1,7,3,6,5] => [4,2,6,3,1,7,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,4,1,7,6,3,5] => [4,2,7,3,1,6,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,5,1,7,3,6,4] => [4,2,6,1,3,7,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,5,1,7,4,6,3] => [4,2,1,6,3,7,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,5,1,7,6,3,4] => [4,2,7,1,3,6,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,5,7,1,3,4,6] => [5,2,6,7,3,1,4] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,6,1,7,3,5,4] => [4,2,6,1,7,3,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,6,1,7,4,5,3] => [4,2,1,6,7,3,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,6,1,7,5,3,4] => [4,2,7,1,6,3,5] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,6,7,1,3,4,5] => [5,2,6,7,1,3,4] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,4,5,6] => [4,2,5,6,7,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,4,6,5] => [4,2,5,6,1,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,5,4,6] => [4,2,5,7,6,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,5,6,4] => [4,2,5,1,6,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,6,4,5] => [4,2,5,7,1,6,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,3,6,5,4] => [4,2,5,1,7,6,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,3,5,6] => [4,2,6,5,7,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,3,6,5] => [4,2,6,5,1,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,5,3,6] => [4,2,7,5,6,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,5,6,3] => [4,2,1,5,6,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,6,3,5] => [4,2,7,5,1,6,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,4,6,5,3] => [4,2,1,5,7,6,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,5,3,4,6] => [4,2,6,7,5,1,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
[2,7,1,5,3,6,4] => [4,2,6,1,5,7,3] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 7
Description
The number of cuts of a poset.
A cut is a subset $A$ of the poset such that the set of lower bounds of the set of upper bounds of $A$ is exactly $A$.
The following 9 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001717The largest size of an interval in a poset. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000264The girth of a graph, which is not a tree. St001060The distinguishing index of a graph. St001879The 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. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001622The number of join-irreducible elements of a lattice.
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