Processing math: 100%

Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001880
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
[1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 4
[1,4,2,3,5] => [1,4,3,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 4
[1,4,3,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 4
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 6
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 5
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 5
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 5
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 6
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 5
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 4
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 4
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 5
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 4
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 5
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 4
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 4
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 4
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 4
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 4
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 4
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 4
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 4
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 4
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => 7
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => 7
[1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => 6
[1,2,3,6,4,5,7] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => 6
[1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => 6
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => 7
[1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => 6
[1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => 5
[1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => 2
[1,2,4,6,5,3,7] => [1,2,6,5,4,3,7] => [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => 5
[1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => 6
[1,2,5,3,6,4,7] => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => 5
[1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => 6
[1,2,5,4,6,3,7] => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => 5
[1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => 5
[1,2,5,6,4,3,7] => [1,2,6,5,4,3,7] => [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => 5
[1,2,6,3,4,5,7] => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => 5
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000264
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 24%●distinct values known / distinct values provided: 14%
Values
[1,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 4 - 1
[1,3,2,4] => [1,3,2,4] => [1,2,3,4] => ([],4)
 => ? = 4 - 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ? = 5 - 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ? = 5 - 1
[1,3,2,4,5] => [1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ? = 5 - 1
[1,3,4,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 4 - 1
[1,4,2,3,5] => [1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 4 - 1
[1,4,3,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 4 - 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ? = 6 - 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ? = 6 - 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ? = 6 - 1
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => ([(4,5)],6)
 => ? = 5 - 1
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => ([(4,5)],6)
 => ? = 5 - 1
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => ([(4,5)],6)
 => ? = 5 - 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ? = 6 - 1
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => ([(4,5)],6)
 => ? = 5 - 1
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,2,4,3,5,6] => ([(4,5)],6)
 => ? = 1 - 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => ([(4,5)],6)
 => ? = 5 - 1
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => ([(4,5)],6)
 => ? = 5 - 1
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7)
 => ? = 7 - 1
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7)
 => ? = 7 - 1
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7)
 => ? = 7 - 1
[1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => ([(5,6)],7)
 => ? = 6 - 1
[1,2,3,6,4,5,7] => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => ([(5,6)],7)
 => ? = 6 - 1
[1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => ([(5,6)],7)
 => ? = 6 - 1
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => ([],7)
 => ? = 7 - 1
[1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => ([(5,6)],7)
 => ? = 6 - 1
[1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [1,2,3,5,4,6,7] => ([(5,6)],7)
 => ? = 2 - 1
[1,2,4,6,5,3,7] => [1,2,6,5,4,3,7] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => ([(5,6)],7)
 => ? = 6 - 1
[1,2,5,3,6,4,7] => [1,2,6,4,5,3,7] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => ([(5,6)],7)
 => ? = 6 - 1
[1,2,5,4,6,3,7] => [1,2,6,4,5,3,7] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,5,6,4,3,7] => [1,2,6,5,4,3,7] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,6,3,4,5,7] => [1,2,6,4,5,3,7] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7)
 => ? = 5 - 1
[1,3,5,6,4,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,3,6,4,5,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,3,6,5,4,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,4,5,6,2,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,4,5,6,3,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,4,6,2,5,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,4,6,3,5,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,4,6,5,2,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,4,6,5,3,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,3,6,2,4,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,3,6,4,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,4,6,2,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,4,6,3,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,6,2,3,4,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,6,2,4,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,6,3,2,4,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,6,3,4,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,6,4,2,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,5,6,4,3,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,3,4,2,5,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,3,4,5,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,3,5,2,4,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,4,2,3,5,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,4,2,5,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,4,3,2,5,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,4,5,2,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,4,5,3,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,5,2,3,4,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,5,2,4,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,5,3,2,4,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,5,3,4,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,5,4,2,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St000718
(load all 2 compositions to match this statistic)
Mapping
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00309: Permutations —inverse toric promotion⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000718: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 71%
Values
[1,2,3] => [2,3,1] => [1,3,2] => ([(1,2)],3)
 => 2 = 3 - 1
[1,2,3,4] => [2,3,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => 3 = 4 - 1
[1,3,2,4] => [2,4,3,1] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => 3 = 4 - 1
[1,2,3,4,5] => [2,3,4,5,1] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => 4 = 5 - 1
[1,2,4,3,5] => [2,3,5,4,1] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4 = 5 - 1
[1,3,2,4,5] => [2,4,3,5,1] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? = 5 - 1
[1,3,4,2,5] => [2,5,3,4,1] => [3,1,2,4,5] => ([(2,4),(3,4)],5)
 => 3 = 4 - 1
[1,4,2,3,5] => [2,4,5,3,1] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 4 - 1
[1,4,3,2,5] => [2,5,4,3,1] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ? = 4 - 1
[1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 5 = 6 - 1
[1,2,3,5,4,6] => [2,3,4,6,5,1] => [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 5 = 6 - 1
[1,2,4,3,5,6] => [2,3,5,4,6,1] => [3,4,6,1,5,2] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ? = 6 - 1
[1,2,4,5,3,6] => [2,3,6,4,5,1] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 4 = 5 - 1
[1,2,5,3,4,6] => [2,3,5,6,4,1] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 5 - 1
[1,2,5,4,3,6] => [2,3,6,5,4,1] => [3,4,2,6,1,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 5 - 1
[1,3,2,4,5,6] => [2,4,3,5,6,1] => [3,5,1,4,6,2] => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ? = 6 - 1
[1,3,4,2,5,6] => [2,5,3,4,6,1] => [3,6,1,4,5,2] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
[1,3,4,5,2,6] => [2,6,3,4,5,1] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6)
 => 3 = 4 - 1
[1,3,5,2,4,6] => [2,5,3,6,4,1] => [3,6,4,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 1 - 1
[1,3,5,4,2,6] => [2,6,3,5,4,1] => [3,2,4,6,1,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,4,2,3,5,6] => [2,4,5,3,6,1] => [3,5,6,1,4,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 5 - 1
[1,4,2,5,3,6] => [2,4,6,3,5,1] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,4,3,2,5,6] => [2,5,4,3,6,1] => [3,6,5,1,4,2] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
[1,4,3,5,2,6] => [2,6,4,3,5,1] => [3,2,5,1,4,6] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,4,5,2,3,6] => [2,5,6,3,4,1] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,4,5,3,2,6] => [2,6,5,3,4,1] => [3,2,6,1,4,5] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,2,3,4,6] => [2,4,5,6,3,1] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 4 - 1
[1,5,2,4,3,6] => [2,4,6,5,3,1] => [3,5,2,6,1,4] => ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,3,2,4,6] => [2,5,4,6,3,1] => [3,6,5,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,3,4,2,6] => [2,6,4,5,3,1] => [3,2,5,6,1,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,4,2,3,6] => [2,5,6,4,3,1] => [3,6,2,5,1,4] => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,5,4,3,2,6] => [2,6,5,4,3,1] => [3,2,6,5,1,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
[1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 6 = 7 - 1
[1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => [3,4,5,6,1,2,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 6 = 7 - 1
[1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => [3,4,5,7,1,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)
 => ? = 7 - 1
[1,2,3,5,6,4,7] => [2,3,4,7,5,6,1] => [3,4,5,1,2,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 5 = 6 - 1
[1,2,3,6,4,5,7] => [2,3,4,6,7,5,1] => [3,4,5,7,1,2,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 6 - 1
[1,2,3,6,5,4,7] => [2,3,4,7,6,5,1] => [3,4,5,2,7,1,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 6 - 1
[1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => [3,4,6,1,5,7,2] => ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
 => ? = 7 - 1
[1,2,4,5,3,6,7] => [2,3,6,4,5,7,1] => [3,4,7,1,5,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 6 - 1
[1,2,4,5,6,3,7] => [2,3,7,4,5,6,1] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 5 - 1
[1,2,4,6,3,5,7] => [2,3,6,4,7,5,1] => [3,4,7,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[1,2,4,6,5,3,7] => [2,3,7,4,6,5,1] => [3,4,2,5,7,1,6] => ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,5,3,4,6,7] => [2,3,5,6,4,7,1] => [3,4,6,7,1,5,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 6 - 1
[1,2,5,3,6,4,7] => [2,3,5,7,4,6,1] => [3,4,6,1,2,5,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,5,4,3,6,7] => [2,3,6,5,4,7,1] => [3,4,7,6,1,5,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 6 - 1
[1,2,5,4,6,3,7] => [2,3,7,5,4,6,1] => [3,4,2,6,1,5,7] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,5,6,3,4,7] => [2,3,6,7,4,5,1] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,5,6,4,3,7] => [2,3,7,6,4,5,1] => [3,4,2,7,1,5,6] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,6,3,4,5,7] => [2,3,5,6,7,4,1] => [3,4,6,7,1,2,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 5 - 1
[1,2,6,3,5,4,7] => [2,3,5,7,6,4,1] => [3,4,6,2,7,1,5] => ([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,6,4,3,5,7] => [2,3,6,5,7,4,1] => [3,4,7,6,1,2,5] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 5 - 1
[1,2,6,4,5,3,7] => [2,3,7,5,6,4,1] => [3,4,2,6,7,1,5] => ([(0,1),(0,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,6,5,3,4,7] => [2,3,6,7,5,4,1] => [3,4,7,2,6,1,5] => ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,2,6,5,4,3,7] => [2,3,7,6,5,4,1] => [3,4,2,7,6,1,5] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,3,2,4,5,6,7] => [2,4,3,5,6,7,1] => [3,5,1,4,6,7,2] => ([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 7 - 1
[1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => [3,5,4,6,1,2,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 6 = 7 - 1
[1,3,4,2,5,6,7] => [2,5,3,4,6,7,1] => [3,6,1,4,5,7,2] => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 6 - 1
[1,3,4,5,2,6,7] => [2,6,3,4,5,7,1] => [3,7,1,4,5,6,2] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5 - 1
[1,3,4,5,6,2,7] => [2,7,3,4,5,6,1] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7)
 => 3 = 4 - 1
[1,3,4,6,2,5,7] => [2,6,3,4,7,5,1] => [3,7,4,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[1,3,4,6,5,2,7] => [2,7,3,4,6,5,1] => [3,2,4,5,7,1,6] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 6 - 1
[1,3,5,2,4,6,7] => [2,5,3,6,4,7,1] => [3,6,4,7,1,5,2] => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2 - 1
[1,3,5,2,6,4,7] => [2,5,3,7,4,6,1] => [3,6,4,1,2,5,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[1,3,5,4,2,6,7] => [2,6,3,5,4,7,1] => [3,7,4,6,1,5,2] => ([(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => ? = 5 - 1
[1,3,5,4,6,2,7] => [2,7,3,5,4,6,1] => [3,2,4,6,1,5,7] => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 6 - 1
Description
The largest Laplacian eigenvalue of a graph if it is integral. This statistic is undefined if the largest Laplacian eigenvalue of the graph is not integral. Various results are collected in Section 3.9 of [1]
Matching statistic: St001040
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
St001040: Perfect matchings ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 43%
Values
[1,2,3] => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [(1,6),(2,5),(3,4)]
 => 4 = 3 + 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [(1,8),(2,7),(3,6),(4,5)]
 => 5 = 4 + 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => [(1,8),(2,3),(4,7),(5,6)]
 => 5 = 4 + 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [(1,10),(2,9),(3,8),(4,7),(5,6)]
 => 6 = 5 + 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [(1,10),(2,3),(4,9),(5,8),(6,7)]
 => 6 = 5 + 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [(1,10),(2,9),(3,4),(5,8),(6,7)]
 => 6 = 5 + 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [(1,10),(2,5),(3,4),(6,9),(7,8)]
 => 5 = 4 + 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,10),(4,5),(6,9),(7,8)]
 => 5 = 4 + 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,10),(4,5),(6,9),(7,8)]
 => 5 = 4 + 1
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]
 => ? = 6 + 1
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]
 => ? = 6 + 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]
 => ? = 6 + 1
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]
 => ? = 5 + 1
[1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
 => ? = 5 + 1
[1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
 => ? = 5 + 1
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]
 => ? = 6 + 1
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]
 => ? = 5 + 1
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]
 => ? = 4 + 1
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]
 => ? = 1 + 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]
 => ? = 4 + 1
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]
 => ? = 5 + 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]
 => ? = 4 + 1
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]
 => ? = 5 + 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]
 => ? = 4 + 1
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]
 => ? = 4 + 1
[1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]
 => ? = 4 + 1
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]
 => 5 = 4 + 1
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]
 => 5 = 4 + 1
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]
 => 5 = 4 + 1
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]
 => 5 = 4 + 1
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]
 => 5 = 4 + 1
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]
 => 5 = 4 + 1
[1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8)]
 => ? = 7 + 1
[1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [(1,14),(2,3),(4,13),(5,12),(6,11),(7,10),(8,9)]
 => ? = 7 + 1
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [(1,14),(2,13),(3,4),(5,12),(6,11),(7,10),(8,9)]
 => ? = 7 + 1
[1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [(1,14),(2,5),(3,4),(6,13),(7,12),(8,11),(9,10)]
 => ? = 6 + 1
[1,2,3,6,4,5,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)]
 => ? = 6 + 1
[1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)]
 => ? = 6 + 1
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9)]
 => ? = 7 + 1
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [(1,14),(2,13),(3,6),(4,5),(7,12),(8,11),(9,10)]
 => ? = 6 + 1
[1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [(1,14),(2,7),(3,6),(4,5),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [(1,2),(3,14),(4,7),(5,6),(8,13),(9,12),(10,11)]
 => ? = 2 + 1
[1,2,4,6,5,3,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [(1,2),(3,14),(4,7),(5,6),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,5,3,4,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)]
 => ? = 6 + 1
[1,2,5,3,6,4,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
 => [(1,14),(2,3),(4,7),(5,6),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)]
 => ? = 6 + 1
[1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
 => [(1,14),(2,3),(4,7),(5,6),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,5,6,3,4,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,4),(2,3),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,5,6,4,3,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,4),(2,3),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,6,3,4,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,2),(3,4),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,6,3,5,4,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,2),(3,4),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,6,4,3,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,2),(3,4),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,6,4,5,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,2),(3,4),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,6,5,3,4,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,2),(3,4),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [(1,2),(3,4),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => ? = 5 + 1
[1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9)]
 => ? = 7 + 1
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [(1,14),(2,13),(3,4),(5,12),(6,7),(8,11),(9,10)]
 => ? = 7 + 1
[1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => [(1,14),(2,13),(3,12),(4,7),(5,6),(8,11),(9,10)]
 => ? = 6 + 1
[1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => [(1,14),(2,13),(3,8),(4,7),(5,6),(9,12),(10,11)]
 => ? = 5 + 1
[1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [(1,14),(2,9),(3,8),(4,7),(5,6),(10,13),(11,12)]
 => ? = 4 + 1
[1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [(1,2),(3,14),(4,9),(5,8),(6,7),(10,13),(11,12)]
 => ? = 2 + 1
[1,3,4,6,5,2,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [(1,2),(3,14),(4,9),(5,8),(6,7),(10,13),(11,12)]
 => ? = 6 + 1
[1,3,5,2,4,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)]
 => ? = 2 + 1
[1,3,5,2,6,4,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
 => [(1,14),(2,3),(4,9),(5,8),(6,7),(10,13),(11,12)]
 => ? = 2 + 1
[1,3,5,4,2,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)]
 => ? = 5 + 1
Description
The depth of the decreasing labelled binary unordered tree associated with the perfect matching. The bijection between perfect matchings of {1,…,2n} and trees with n+1 leaves is described in Example 5.2.6 of [1].