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Your data matches 70 different statistics following compositions of up to 3 maps.
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Matching statistic: St000264
Mp00223: Permutations —runsort⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,4,5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[1,4,5,3,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[1,5,2,4,3] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,3,2,4] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,1,4,5,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,3,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,4,1,5,3] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,4,3,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,1,4,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[3,1,5,2,4] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,2,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[3,2,4,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,2,5,6,3,4] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[1,2,5,6,4,3] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[1,2,6,3,5,4] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,2,6,4,3,5] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,4,6,2,5] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,4,6,5,2] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,5,2,6,4] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,5,4,2,6] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,5,6,2,4] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,3,5,6,4,2] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,3,6,2,4,5] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,2,5,4] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
[1,3,6,4,2,5] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
[1,3,6,4,5,2] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,5,2,4] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,5,4,2] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,2,5,6,3] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,2,6,3,5] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,2,6,5,3] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,3,2,5,6] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,3,2,6,5] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,3,5,2,6] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,5,2,3,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[1,4,5,2,6,3] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,4,5,3,2,6] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,4,5,3,6,2] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[1,4,5,6,2,3] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[1,4,5,6,3,2] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[1,4,6,2,3,5] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,4,6,3,5,2] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,4,6,5,2,3] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,4,6,5,3,2] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,5,2,3,6,4] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,5,2,4,3,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,5,2,4,6,3] => [1,5,2,4,6,3] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
[1,5,2,6,3,4] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,5,2,6,4,3] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
[1,5,3,2,4,6] => [1,5,2,4,6,3] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St000298
Mp00109: Permutations —descent word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000298: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000298: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[1,4,5,3,2] => 0011 => 0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,5,3,2,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[2,1,4,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[2,3,1,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[2,4,3,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[3,1,4,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[3,2,1,4,5] => 1100 => 1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,2,5,6,3,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,2,5,6,4,3] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,2,6,3,5,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,2,6,4,3,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,4,6,2,5] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,4,6,5,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,5,2,6,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,5,4,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,5,6,2,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,5,6,4,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,4,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,5,4] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,3,6,4,2,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 4 - 2
[1,3,6,4,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,6,5,2,4] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,6,5,4,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,4,2,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,2,6,5,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,4,3,2,5,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,3,2,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,5,2,3,6] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,4,5,2,6,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,5,3,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,5,3,6,2] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,4,5,6,2,3] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,4,5,6,3,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,4,6,2,3,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,4,6,3,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,6,5,2,3] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,6,5,3,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,5,2,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,6,4,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,3,2,4,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,3,2,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,4,2] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,4,2,3,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,4,2,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,4,3,2,6] => 01110 => 00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 3 - 2
[1,5,4,3,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,6,2,3,4] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,5,6,2,4,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
Description
The order dimension or Dushnik-Miller dimension of a poset.
This is the minimal number of linear orderings whose intersection is the given poset.
Matching statistic: St000307
Mp00109: Permutations —descent word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000307: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000307: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[1,4,5,3,2] => 0011 => 0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,5,3,2,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[2,1,4,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[2,3,1,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[2,4,3,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[3,1,4,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[3,2,1,4,5] => 1100 => 1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,2,5,6,3,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,2,5,6,4,3] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,2,6,3,5,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,2,6,4,3,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,4,6,2,5] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,4,6,5,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,5,2,6,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,5,4,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,5,6,2,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,5,6,4,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,4,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,5,4] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,3,6,4,2,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 4 - 2
[1,3,6,4,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,6,5,2,4] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,6,5,4,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,4,2,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,2,6,5,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,4,3,2,5,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,3,2,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,5,2,3,6] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,4,5,2,6,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,5,3,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,5,3,6,2] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,4,5,6,2,3] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,4,5,6,3,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,4,6,2,3,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,4,6,3,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,6,5,2,3] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,6,5,3,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,5,2,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,6,4,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,3,2,4,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,3,2,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,4,2] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,4,2,3,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,4,2,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,4,3,2,6] => 01110 => 00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 3 - 2
[1,5,4,3,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,6,2,3,4] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,5,6,2,4,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
Description
The number of rowmotion orbits of a poset.
Rowmotion is an operation on order ideals in a poset $P$. It sends an order ideal $I$ to the order ideal generated by the minimal antichain of $P \setminus I$.
Matching statistic: St000845
Mp00109: Permutations —descent word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000845: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000845: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[1,4,5,3,2] => 0011 => 0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,5,3,2,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[2,1,4,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[2,3,1,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[2,4,3,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[3,1,4,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[3,2,1,4,5] => 1100 => 1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,2,5,6,3,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,2,5,6,4,3] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,2,6,3,5,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,2,6,4,3,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,4,6,2,5] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,4,6,5,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,5,2,6,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,5,4,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,5,6,2,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,5,6,4,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,4,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,5,4] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,3,6,4,2,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 4 - 2
[1,3,6,4,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,6,5,2,4] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,6,5,4,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,4,2,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,2,6,5,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,4,3,2,5,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,3,2,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,5,2,3,6] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,4,5,2,6,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,5,3,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,5,3,6,2] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,4,5,6,2,3] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,4,5,6,3,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,4,6,2,3,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,4,6,3,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,6,5,2,3] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,6,5,3,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,5,2,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,6,4,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,3,2,4,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,3,2,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,4,2] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,4,2,3,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,4,2,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,4,3,2,6] => 01110 => 00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 3 - 2
[1,5,4,3,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,6,2,3,4] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,5,6,2,4,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
Description
The maximal number of elements covered by an element in a poset.
Matching statistic: St000846
Mp00109: Permutations —descent word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000846: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000846: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[1,4,5,3,2] => 0011 => 0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,5,3,2,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[2,1,4,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[2,3,1,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[2,4,3,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[3,1,4,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[3,2,1,4,5] => 1100 => 1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,2,5,6,3,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,2,5,6,4,3] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,2,6,3,5,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,2,6,4,3,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,4,6,2,5] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,4,6,5,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,5,2,6,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,5,4,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,5,6,2,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,5,6,4,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,4,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,5,4] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,3,6,4,2,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 4 - 2
[1,3,6,4,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,6,5,2,4] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,6,5,4,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,4,2,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,2,6,5,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,4,3,2,5,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,3,2,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,5,2,3,6] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,4,5,2,6,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,5,3,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,5,3,6,2] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,4,5,6,2,3] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,4,5,6,3,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,4,6,2,3,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,4,6,3,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,6,5,2,3] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,6,5,3,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,5,2,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,6,4,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,3,2,4,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,3,2,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,4,2] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,4,2,3,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,4,2,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,4,3,2,6] => 01110 => 00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 3 - 2
[1,5,4,3,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,6,2,3,4] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,5,6,2,4,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
Description
The maximal number of elements covering an element of a poset.
Matching statistic: St001632
Mp00109: Permutations —descent word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St001632: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St001632: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[1,4,5,3,2] => 0011 => 0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,5,3,2,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[2,1,4,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[2,3,1,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 2
[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[2,4,3,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 2
[3,1,4,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 2
[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[3,2,1,4,5] => 1100 => 1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 2
[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 3 - 2
[1,2,5,6,3,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,2,5,6,4,3] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,2,6,3,5,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,2,6,4,3,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,4,6,2,5] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,4,6,5,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,5,2,6,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,5,4,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,5,6,2,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,3,5,6,4,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,4,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,3,6,2,5,4] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,3,6,4,2,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 4 - 2
[1,3,6,4,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,3,6,5,2,4] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,3,6,5,4,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,4,2,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,2,6,5,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,4,3,2,5,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,3,2,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,4,5,2,3,6] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,4,5,2,6,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,5,3,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,5,3,6,2] => 00101 => 01111 => ([(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)
=> ? = 4 - 2
[1,4,5,6,2,3] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 2
[1,4,5,6,3,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 2
[1,4,6,2,3,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 2
[1,4,6,3,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,4,6,5,2,3] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,4,6,5,3,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 2
[1,5,2,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,2,6,4,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,3,2,4,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,3,2,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,5,3,6,4,2] => 01011 => 00001 => ([(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)
=> ? = 3 - 2
[1,5,4,2,3,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 2
[1,5,4,2,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,4,3,2,6] => 01110 => 00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 3 - 2
[1,5,4,3,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 2
[1,5,6,2,3,4] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 2
[1,5,6,2,4,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 2
[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 3 - 2
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
Matching statistic: St000632
Mp00109: Permutations —descent word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000632: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000632: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 3
[1,4,5,3,2] => 0011 => 0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 3
[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 3 - 3
[1,5,3,2,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 3
[2,1,4,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 3
[2,3,1,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 3
[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 3 - 3
[2,4,3,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 3
[3,1,4,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 3
[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 3 - 3
[3,2,1,4,5] => 1100 => 1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 3
[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 3 - 3
[1,2,5,6,3,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 3
[1,2,5,6,4,3] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 3
[1,2,6,3,5,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,2,6,4,3,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,3,4,6,2,5] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,3,4,6,5,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 3
[1,3,5,2,6,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,3,5,4,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,3,5,6,2,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,3,5,6,4,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 3
[1,3,6,2,4,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 3
[1,3,6,2,5,4] => 00101 => 01111 => ([(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)
=> ? = 4 - 3
[1,3,6,4,2,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 4 - 3
[1,3,6,4,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,3,6,5,2,4] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,3,6,5,4,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 3
[1,4,2,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,4,2,6,5,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 3
[1,4,3,2,5,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,4,3,2,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,4,5,2,3,6] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 3
[1,4,5,2,6,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,4,5,3,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,4,5,3,6,2] => 00101 => 01111 => ([(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)
=> ? = 4 - 3
[1,4,5,6,2,3] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 3
[1,4,5,6,3,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 3
[1,4,6,2,3,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 3
[1,4,6,3,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,4,6,5,2,3] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,4,6,5,3,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 3
[1,5,2,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,5,2,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,5,2,6,4,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 3
[1,5,3,2,4,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,5,3,2,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,5,3,6,4,2] => 01011 => 00001 => ([(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)
=> ? = 3 - 3
[1,5,4,2,3,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,5,4,2,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,4,3,2,6] => 01110 => 00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 3 - 3
[1,5,4,3,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,6,2,3,4] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 3
[1,5,6,2,4,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
Description
The jump number of the poset.
A jump in a linear extension $e_1, \dots, e_n$ of a poset $P$ is a pair $(e_i, e_{i+1})$ so that $e_{i+1}$ does not cover $e_i$ in $P$. The jump number of a poset is the minimal number of jumps in linear extensions of a poset.
Matching statistic: St001633
Mp00109: Permutations —descent word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St001633: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St001633: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 3
[1,4,5,3,2] => 0011 => 0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 3
[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 3 - 3
[1,5,3,2,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 3
[2,1,4,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 3
[2,3,1,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 - 3
[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 3 - 3
[2,4,3,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 3
[3,1,4,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 - 3
[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 3 - 3
[3,2,1,4,5] => 1100 => 1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 4 - 3
[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 3 - 3
[1,2,5,6,3,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 3
[1,2,5,6,4,3] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 3
[1,2,6,3,5,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,2,6,4,3,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,3,4,6,2,5] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,3,4,6,5,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 3
[1,3,5,2,6,4] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,3,5,4,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,3,5,6,2,4] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,3,5,6,4,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 3
[1,3,6,2,4,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 3
[1,3,6,2,5,4] => 00101 => 01111 => ([(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)
=> ? = 4 - 3
[1,3,6,4,2,5] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 4 - 3
[1,3,6,4,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,3,6,5,2,4] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,3,6,5,4,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 3
[1,4,2,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,4,2,6,5,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 3
[1,4,3,2,5,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,4,3,2,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,4,5,2,3,6] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 3
[1,4,5,2,6,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,4,5,3,2,6] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,4,5,3,6,2] => 00101 => 01111 => ([(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)
=> ? = 4 - 3
[1,4,5,6,2,3] => 00010 => 01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 4 - 3
[1,4,5,6,3,2] => 00011 => 01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 4 - 3
[1,4,6,2,3,5] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 3 - 3
[1,4,6,3,5,2] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,4,6,5,2,3] => 00110 => 01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,4,6,5,3,2] => 00111 => 01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 3 - 3
[1,5,2,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,5,2,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,5,2,6,4,3] => 01011 => 00001 => ([(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)
=> ? = 3 - 3
[1,5,3,2,4,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,5,3,2,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,5,3,6,4,2] => 01011 => 00001 => ([(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)
=> ? = 3 - 3
[1,5,4,2,3,6] => 01100 => 00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 3 - 3
[1,5,4,2,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,4,3,2,6] => 01110 => 00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 3 - 3
[1,5,4,3,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 3 - 3
[1,5,6,2,3,4] => 00100 => 01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 4 - 3
[1,5,6,2,4,3] => 00101 => 01111 => ([(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)
=> ? = 3 - 3
[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 3 - 3
Description
The number of simple modules with projective dimension two in the incidence algebra of the poset.
Matching statistic: St000741
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00223: Permutations —runsort⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000741: Graphs ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000741: Graphs ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
[1,4,5,3,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
[1,5,2,4,3] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
[1,5,3,2,4] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
[2,1,4,5,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
[2,3,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
[2,4,1,5,3] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
[2,4,3,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
[3,1,4,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
[3,1,5,2,4] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
[3,2,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
[3,2,4,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
[1,2,5,6,3,4] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,2,5,6,4,3] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,2,6,3,5,4] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,2,6,4,3,5] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,4,6,2,5] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,4,6,5,2] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,5,2,6,4] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,5,4,2,6] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,5,6,2,4] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,5,6,4,2] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,6,2,4,5] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,6,2,5,4] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,3,6,4,2,5] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,3,6,4,5,2] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,6,5,2,4] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,3,6,5,4,2] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,2,5,6,3] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,2,6,3,5] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,2,6,5,3] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,3,2,5,6] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,3,2,6,5] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,3,5,2,6] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,5,2,3,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,4,5,2,6,3] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,5,3,2,6] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,5,3,6,2] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,4,5,6,2,3] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,4,5,6,3,2] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,4,6,2,3,5] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,6,3,5,2] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,6,5,2,3] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,4,6,5,3,2] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,2,3,6,4] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,2,4,3,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,2,4,6,3] => [1,5,2,4,6,3] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,2,6,3,4] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,2,6,4,3] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,3,2,4,6] => [1,5,2,4,6,3] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,3,2,6,4] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,3,4,2,6] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,3,6,2,4] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,3,6,4,2] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,4,2,3,6] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,4,2,6,3] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,4,3,2,6] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,4,3,6,2] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,5,6,2,3,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,5,6,2,4,3] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[1,5,6,3,2,4] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[1,5,6,3,4,2] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,5,6,4,2,3] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,5,6,4,3,2] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,6,2,3,5,4] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,6,2,4,3,5] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,6,2,4,5,3] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,6,2,5,3,4] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,6,2,5,4,3] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,6,3,2,4,5] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[2,1,4,5,3,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,1,4,5,6,3] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,1,5,6,3,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,1,5,6,4,3] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,3,1,4,5,6] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,3,1,5,6,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,3,4,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,3,6,1,4,5] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,4,1,5,6,3] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[2,4,3,1,5,6] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[2,5,1,3,6,4] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[2,5,4,1,3,6] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[2,5,6,3,4,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[2,5,6,4,3,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,1,2,5,6,4] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,1,4,5,6,2] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,1,5,6,2,4] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[3,1,5,6,4,2] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,2,1,4,5,6] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,2,1,5,6,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,2,4,1,5,6] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[3,2,5,6,4,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,4,1,2,5,6] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,4,1,5,6,2] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,4,2,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,4,2,5,6,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,6,1,4,5,2] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[3,6,2,1,4,5] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[4,1,2,5,6,3] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[4,1,3,6,2,5] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
Description
The Colin de Verdière graph invariant.
Matching statistic: St000454
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00065: Permutations —permutation poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
[1,4,5,2,3] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 3 - 1
[2,1,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4 - 1
[2,3,1,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4 - 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 1
[3,1,4,5,2] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4 - 1
[3,1,5,2,4] => [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 1
[3,2,1,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[3,2,4,1,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2 = 3 - 1
[1,2,5,6,3,4] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,2,5,6,4,3] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,2,6,3,5,4] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,2,6,4,3,5] => [1,2,3,6,5,4] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 3 - 1
[1,3,4,6,2,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 3 - 1
[1,3,4,6,5,2] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 3 - 1
[1,3,5,2,6,4] => [1,2,3,5,6,4] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,5,4,2,6] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,5,6,2,4] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,5,6,4,2] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,6,2,4,5] => [1,2,3,6,5,4] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 3 - 1
[1,3,6,2,5,4] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,3,6,4,2,5] => [1,2,3,6,5,4] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 4 - 1
[1,3,6,4,5,2] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,6,5,2,4] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,6,5,4,2] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,4,2,5,6,3] => [1,2,4,5,6,3] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 3 - 1
[1,4,2,6,3,5] => [1,2,4,6,5,3] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[1,4,2,6,5,3] => [1,2,4,6,3,5] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,4,3,2,5,6] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[1,4,3,2,6,5] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[1,4,3,5,2,6] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,4,5,2,3,6] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,4,5,2,6,3] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[1,4,5,3,2,6] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[1,4,5,3,6,2] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
[1,4,5,6,2,3] => [1,2,4,6,3,5] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,4,5,6,3,2] => [1,2,4,6,3,5] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,4,6,2,3,5] => [1,2,4,3,6,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,4,6,3,5,2] => [1,2,4,3,6,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,4,6,5,2,3] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,4,6,5,3,2] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,5,2,3,6,4] => [1,2,5,6,4,3] => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 3 - 1
[1,5,2,4,3,6] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,5,2,4,6,3] => [1,2,5,6,3,4] => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,5,2,6,3,4] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,5,2,6,4,3] => [1,2,5,4,6,3] => ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,5,3,2,4,6] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
[1,5,3,2,6,4] => [1,2,5,6,4,3] => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 3 - 1
[1,5,3,4,2,6] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,5,3,6,2,4] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,6,5,2,4,3] => [1,2,6,3,5,4] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,4,1,6,3,5] => [1,2,4,6,5,3] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,4,3,6,1,5] => [1,2,4,6,5,3] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,6,5,1,4,3] => [1,2,6,3,5,4] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[3,1,4,5,2,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[3,2,4,5,1,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[4,1,2,6,3,5] => [1,4,6,5,3,2] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,3,5,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[4,2,1,6,3,5] => [1,4,6,5,3,2] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,2,3,5,1,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[4,3,1,5,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[4,3,2,5,1,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[5,1,3,6,2,4] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[5,1,4,3,2,6] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[5,1,4,6,2,3] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[5,2,4,3,1,6] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[5,3,1,4,2,6] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[5,3,1,6,2,4] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[5,3,2,4,1,6] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[5,3,2,6,1,4] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2 = 3 - 1
[6,1,5,2,4,3] => [1,6,3,5,4,2] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[1,2,6,3,5,7,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[1,2,6,5,3,7,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[1,2,6,5,4,7,3] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[1,3,6,2,5,7,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[1,3,6,4,5,7,2] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[1,3,6,5,2,7,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[1,3,6,5,4,7,2] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[1,4,2,5,7,3,6] => [1,2,4,5,7,6,3] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,4,3,5,7,2,6] => [1,2,4,5,7,6,3] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,7,2,6,4,5,3] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,7,2,6,5,4,3] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,7,3,6,4,5,2] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,7,3,6,5,4,2] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,7,4,6,2,5,3] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,7,4,6,3,5,2] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,7,4,6,5,2,3] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[1,7,4,6,5,3,2] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[2,1,6,3,5,7,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[2,1,6,5,3,7,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[2,1,6,5,4,7,3] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[2,3,6,1,5,7,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[2,3,6,5,1,7,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2 = 3 - 1
[2,4,1,5,7,3,6] => [1,2,4,5,7,6,3] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[2,4,3,5,7,1,6] => [1,2,4,5,7,6,3] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[2,7,1,6,4,5,3] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 1
[2,7,1,6,5,4,3] => [1,2,7,3,4,6,5] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 3 - 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.
The following 60 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001330The hat guessing number of a graph. St001644The dimension of a graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000422The energy of a graph, if it is integral. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000908The length of the shortest maximal antichain in a poset. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001268The size of the largest ordinal summand in the poset. St001399The distinguishing number of a poset. St001510The number of self-evacuating linear extensions of a finite poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001534The alternating sum of the coefficients of the Poincare polynomial of the poset cone. St001779The order of promotion on the set of linear extensions of a poset. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000850The number of 1/2-balanced pairs in a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001301The first Betti number of the order complex associated with the poset. St001396Number of triples of incomparable elements in a finite poset. St001397Number of pairs of incomparable elements in a finite poset. St001398Number of subsets of size 3 of elements in a poset that form a "v". St001902The number of potential covers of a poset. St001964The interval resolution global dimension of a poset. St001472The permanent of the Coxeter matrix of the poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001635The trace of the square of the Coxeter matrix of the incidence algebra of a poset. St001645The pebbling number of a connected graph. St000896The number of zeros on the main diagonal of an alternating sign matrix. St000754The Grundy value for the game of removing nestings in a perfect matching. St001115The number of even descents of a permutation. St001618The cardinality of the Frattini sublattice of a lattice. St001845The number of join irreducibles minus the rank of a lattice. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001613The binary logarithm of the size of the center of a lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001881The number of factors of a lattice as a Cartesian product of lattices. St001846The number of elements which do not have a complement in the lattice. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001833The number of linear intervals in a lattice. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001620The number of sublattices of a lattice. St001679The number of subsets of a lattice whose meet is the bottom element. St000007The number of saliances of the permutation. St001434The number of negative sum pairs of a signed permutation.
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