- FindStat

Your data matches 19 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001200

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1,2,3] => [1,2] => [1,2] => [1,0,1,0]
 => 2
[1,3,2] => [1,2] => [1,2] => [1,0,1,0]
 => 2
[3,1,2] => [1,2] => [1,2] => [1,0,1,0]
 => 2
[1,2,3,4] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 3
[1,2,4,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 3
[1,3,2,4] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 2
[1,3,4,2] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 2
[1,4,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 3
[1,4,3,2] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 2
[2,1,3,4] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 2
[2,1,4,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 2
[2,4,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 2
[4,1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 3
[4,1,3,2] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 2
[4,2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 2
[1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 3
[1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 3
[1,2,4,3,5] => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 3
[1,2,4,5,3] => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 3
[1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 3
[1,2,5,4,3] => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 3
[1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[1,3,4,2,5] => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,3,4,5,2] => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[1,3,5,4,2] => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,4,2,3,5] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,4,2,5,3] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,4,3,2,5] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,4,3,5,2] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,4,5,2,3] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,4,5,3,2] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 3
[1,5,2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 3
[1,5,3,2,4] => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[1,5,3,4,2] => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,5,4,2,3] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[1,5,4,3,2] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[2,1,3,4,5] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 3
[2,1,3,5,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 3
[2,1,4,3,5] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
 => 2
[2,1,4,5,3] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
 => 2
[2,1,5,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 3
[2,1,5,4,3] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
 => 2
[2,3,1,4,5] => [2,3,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => 2
[2,3,1,5,4] => [2,3,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => 2
[2,3,5,1,4] => [2,3,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => 2
[2,4,1,3,5] => [2,4,1,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
 => 2
[2,4,1,5,3] => [2,4,1,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
 => 2

Description

The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.

Matching statistic: St000260
(load all 2 compositions to match this statistic)

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [1,2] => ([],2)
 => ? = 2
[1,3,2] => [1,2] => ([],2)
 => ? = 2
[3,1,2] => [1,2] => ([],2)
 => ? = 2
[1,2,3,4] => [1,2,3] => ([],3)
 => ? = 3
[1,2,4,3] => [1,2,3] => ([],3)
 => ? = 3
[1,3,2,4] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[1,3,4,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[1,4,2,3] => [1,2,3] => ([],3)
 => ? = 3
[1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[2,1,3,4] => [2,1,3] => ([(1,2)],3)
 => ? = 2
[2,1,4,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2
[2,4,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2
[4,1,2,3] => [1,2,3] => ([],3)
 => ? = 3
[4,1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[4,2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2
[1,2,3,4,5] => [1,2,3,4] => ([],4)
 => ? = 3
[1,2,3,5,4] => [1,2,3,4] => ([],4)
 => ? = 3
[1,2,4,3,5] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,2,4,5,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,2,5,3,4] => [1,2,3,4] => ([],4)
 => ? = 3
[1,2,5,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,3,2,4,5] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3
[1,3,2,5,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3
[1,3,4,2,5] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2
[1,3,4,5,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2
[1,3,5,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3
[1,3,5,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2
[1,4,2,3,5] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2
[1,4,2,5,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2
[1,4,3,2,5] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,4,3,5,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,4,5,2,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2
[1,4,5,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,5,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3
[1,5,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,5,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3
[1,5,3,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2
[1,5,4,2,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2
[1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[2,1,3,4,5] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3
[2,1,3,5,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3
[2,1,4,3,5] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2
[2,1,4,5,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2
[2,1,5,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3
[2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2
[2,3,1,4,5] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2
[2,3,1,5,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2
[2,3,5,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2
[2,4,1,3,5] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,4,1,5,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,4,5,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,5,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3
[2,5,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2
[2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[5,2,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,3,5,1,4,6] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,3,5,1,6,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,3,5,6,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,3,6,5,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,4,1,5,3,6] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[2,4,1,5,6,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[2,4,1,6,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[2,4,5,1,3,6] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[2,4,5,1,6,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[2,4,5,6,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[2,4,6,1,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[2,4,6,5,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[2,5,1,3,4,6] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,5,1,3,6,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,5,1,4,3,6] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,1,4,6,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,1,6,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,5,1,6,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,3,1,4,6] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,3,1,6,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,3,6,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,4,1,3,6] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,4,1,6,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,4,6,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,6,1,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,5,6,1,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,6,3,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,6,4,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,6,3,5,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,6,4,1,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[2,6,4,5,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[2,6,5,1,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[2,6,5,1,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[2,6,5,3,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,6,5,4,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,1,5,2,4,6] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[3,1,5,2,6,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[3,1,5,6,2,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[3,1,6,5,2,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[3,2,5,1,4,6] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[3,2,5,1,6,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[3,2,5,6,1,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[3,2,6,5,1,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[3,5,1,2,4,6] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[3,5,1,2,6,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2

Description

The radius of a connected graph. This is the minimum eccentricity of any vertex.

Matching statistic: St000771
(load all 2 compositions to match this statistic)

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [1,2] => ([],2)
 => ? = 2 - 1
[1,3,2] => [1,2] => ([],2)
 => ? = 2 - 1
[3,1,2] => [1,2] => ([],2)
 => ? = 2 - 1
[1,2,3,4] => [1,2,3] => ([],3)
 => ? = 3 - 1
[1,2,4,3] => [1,2,3] => ([],3)
 => ? = 3 - 1
[1,3,2,4] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 1
[1,3,4,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 1
[1,4,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 1
[1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 1
[2,1,3,4] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 1
[2,1,4,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 1
[2,4,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 1
[4,1,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 1
[4,1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 1
[4,2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 1
[1,2,3,4,5] => [1,2,3,4] => ([],4)
 => ? = 3 - 1
[1,2,3,5,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 1
[1,2,4,3,5] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 1
[1,2,4,5,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 1
[1,2,5,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 1
[1,2,5,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 1
[1,3,2,4,5] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 1
[1,3,2,5,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 1
[1,3,4,2,5] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,3,4,5,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,3,5,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 1
[1,3,5,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,2,3,5] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,2,5,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,3,2,5] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,3,5,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,5,2,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,5,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
[1,5,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 1
[1,5,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 1
[1,5,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 1
[1,5,3,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,5,4,2,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
[2,1,3,4,5] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 1
[2,1,3,5,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 1
[2,1,4,3,5] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 1
[2,1,4,5,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 1
[2,1,5,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 1
[2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 1
[2,3,1,4,5] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[2,3,1,5,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[2,3,5,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[2,4,1,3,5] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[2,4,1,5,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[2,4,5,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[2,5,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 1
[2,5,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 1
[2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[5,2,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[2,3,5,1,4,6] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,3,5,1,6,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,3,5,6,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,3,6,5,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,4,1,5,3,6] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,4,1,5,6,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,4,1,6,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,4,5,1,3,6] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,4,5,1,6,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,4,5,6,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,4,6,1,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,4,6,5,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,3,4,6] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,3,6,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,4,3,6] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,4,6,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,6,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,6,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,3,1,4,6] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,3,1,6,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,3,6,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,4,1,3,6] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,4,1,6,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,4,6,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,6,1,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,5,6,1,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,6,3,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,6,4,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,6,3,5,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,6,4,1,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,6,4,5,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,6,5,1,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,6,5,1,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,6,5,3,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,6,5,4,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,1,5,2,4,6] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[3,1,5,2,6,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[3,1,5,6,2,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[3,1,6,5,2,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[3,2,5,1,4,6] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,2,5,1,6,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,2,5,6,1,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,2,6,5,1,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,5,1,2,4,6] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,5,1,2,6,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1

Description

The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $2$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.

Matching statistic: St000772
(load all 5 compositions to match this statistic)

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [1,2] => ([],2)
 => ? = 2 - 1
[1,3,2] => [1,2] => ([],2)
 => ? = 2 - 1
[3,1,2] => [1,2] => ([],2)
 => ? = 2 - 1
[1,2,3,4] => [1,2,3] => ([],3)
 => ? = 3 - 1
[1,2,4,3] => [1,2,3] => ([],3)
 => ? = 3 - 1
[1,3,2,4] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 1
[1,3,4,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 1
[1,4,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 1
[1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 1
[2,1,3,4] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 1
[2,1,4,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 1
[2,4,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 1
[4,1,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 1
[4,1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 1
[4,2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 1
[1,2,3,4,5] => [1,2,3,4] => ([],4)
 => ? = 3 - 1
[1,2,3,5,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 1
[1,2,4,3,5] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 1
[1,2,4,5,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 1
[1,2,5,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 1
[1,2,5,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 1
[1,3,2,4,5] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 1
[1,3,2,5,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 1
[1,3,4,2,5] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,3,4,5,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,3,5,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 1
[1,3,5,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,2,3,5] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,2,5,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,3,2,5] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,3,5,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,5,2,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,4,5,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
[1,5,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 1
[1,5,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 1
[1,5,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 1
[1,5,3,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,5,4,2,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
[2,1,3,4,5] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 1
[2,1,3,5,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 1
[2,1,4,3,5] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 1
[2,1,4,5,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 1
[2,1,5,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 1
[2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 1
[2,3,1,4,5] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[2,3,1,5,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[2,3,5,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 - 1
[2,4,1,3,5] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[2,4,1,5,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[2,4,5,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[2,5,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 1
[2,5,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 1
[2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[5,2,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
[2,3,5,1,4,6] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,3,5,1,6,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,3,5,6,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,3,6,5,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,4,1,5,3,6] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,4,1,5,6,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,4,1,6,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,4,5,1,3,6] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,4,5,1,6,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,4,5,6,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,4,6,1,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,4,6,5,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,3,4,6] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,3,6,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,4,3,6] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,4,6,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,6,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,5,1,6,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,3,1,4,6] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,3,1,6,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,3,6,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,4,1,3,6] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,4,1,6,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,4,6,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,6,1,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,5,6,1,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,6,3,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,5,6,4,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,6,3,5,1,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,6,4,1,5,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[2,6,4,5,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,6,5,1,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
[2,6,5,1,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,6,5,3,1,4] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[2,6,5,4,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,1,5,2,4,6] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[3,1,5,2,6,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[3,1,5,6,2,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[3,1,6,5,2,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
[3,2,5,1,4,6] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,2,5,1,6,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,2,5,6,1,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,2,6,5,1,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,5,1,2,4,6] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[3,5,1,2,6,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1

Description

The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $1$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$. The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].

Matching statistic: St000259

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [1,2] => [1,2] => ([],2)
 => ? = 2
[1,3,2] => [1,2] => [1,2] => ([],2)
 => ? = 2
[3,1,2] => [1,2] => [1,2] => ([],2)
 => ? = 2
[1,2,3,4] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3
[1,2,4,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3
[1,3,2,4] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[1,3,4,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[1,4,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3
[1,4,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[2,1,3,4] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2
[2,1,4,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2
[2,4,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2
[4,1,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3
[4,1,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[4,2,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2
[1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3
[1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3
[1,2,4,3,5] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,2,4,5,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3
[1,2,5,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3
[1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3
[1,3,4,2,5] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,3,4,5,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3
[1,3,5,4,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,4,2,3,5] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,4,2,5,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,4,3,2,5] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,4,3,5,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,4,5,2,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,4,5,3,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3
[1,5,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,5,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3
[1,5,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,5,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,5,4,3,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[2,1,3,4,5] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3
[2,1,3,5,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3
[2,1,4,3,5] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2
[2,1,4,5,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2
[2,1,5,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3
[2,1,5,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2
[2,3,1,4,5] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[2,3,1,5,4] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[2,3,5,1,4] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[2,4,1,3,5] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,4,1,5,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,4,5,1,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,5,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3
[2,5,1,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2
[2,5,4,1,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[5,2,4,1,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,3,5,1,4,6] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,3,5,1,6,4] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,3,5,6,1,4] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,3,6,5,1,4] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,4,1,5,3,6] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,4,1,5,6,3] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,4,1,6,5,3] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,4,5,1,3,6] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,4,5,1,6,3] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,4,5,6,1,3] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,4,6,1,5,3] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,4,6,5,1,3] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,1,3,4,6] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,1,3,6,4] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,1,4,3,6] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,1,4,6,3] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,1,6,3,4] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,1,6,4,3] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,3,1,4,6] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,3,1,6,4] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,3,6,1,4] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,4,1,3,6] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,4,1,6,3] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,4,6,1,3] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,6,1,3,4] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,6,1,4,3] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,5,6,3,1,4] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,5,6,4,1,3] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,6,3,5,1,4] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,6,4,1,5,3] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,6,4,5,1,3] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,6,5,1,3,4] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,6,5,1,4,3] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[2,6,5,3,1,4] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[2,6,5,4,1,3] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[3,1,5,2,4,6] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,1,5,2,6,4] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,1,5,6,2,4] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,1,6,5,2,4] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,2,5,1,4,6] => [3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,2,5,1,6,4] => [3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,2,5,6,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,2,6,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,5,1,2,4,6] => [3,5,1,2,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
[3,5,1,2,6,4] => [3,5,1,2,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2

Description

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

Matching statistic: St000302

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000302: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [1,2] => [1,2] => ([],2)
 => ? = 2 - 2
[1,3,2] => [1,2] => [1,2] => ([],2)
 => ? = 2 - 2
[3,1,2] => [1,2] => [1,2] => ([],2)
 => ? = 2 - 2
[1,2,3,4] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 2
[1,2,4,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 2
[1,3,2,4] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 2
[1,3,4,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 2
[1,4,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 2
[1,4,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 2
[2,1,3,4] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 2
[2,1,4,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 2
[2,4,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 2
[4,1,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 2
[4,1,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 - 2
[4,2,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 2 - 2
[1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 2
[1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 2
[1,2,4,3,5] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 2
[1,2,4,5,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 2
[1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 2
[1,2,5,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 2
[1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 2
[1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 2
[1,3,4,2,5] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,3,4,5,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 2
[1,3,5,4,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,4,2,3,5] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,4,2,5,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,4,3,2,5] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,4,3,5,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,4,5,2,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,4,5,3,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 2
[1,5,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 - 2
[1,5,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 2
[1,5,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,5,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[1,5,4,3,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[2,1,3,4,5] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 2
[2,1,3,5,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 2
[2,1,4,3,5] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 2
[2,1,4,5,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 2
[2,1,5,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 2
[2,1,5,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 2
[2,3,1,4,5] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[2,3,1,5,4] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[2,3,5,1,4] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 2
[2,4,1,3,5] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 2 - 2
[2,4,1,5,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 2 - 2
[2,4,5,1,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 2 - 2
[2,5,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 - 2
[2,5,1,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 2 - 2
[2,5,4,1,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 2 - 2
[5,2,4,1,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 2 - 2
[2,3,5,1,4,6] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,3,5,1,6,4] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,3,5,6,1,4] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,3,6,5,1,4] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,4,1,5,3,6] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,4,1,5,6,3] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,4,1,6,5,3] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,4,5,1,3,6] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,4,5,1,6,3] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,4,5,6,1,3] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,4,6,1,5,3] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,4,6,5,1,3] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,1,3,4,6] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,1,3,6,4] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,1,4,3,6] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,1,4,6,3] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,1,6,3,4] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,1,6,4,3] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,3,1,4,6] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,3,1,6,4] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,3,6,1,4] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,4,1,3,6] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,4,1,6,3] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,4,6,1,3] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,6,1,3,4] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,6,1,4,3] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,6,3,1,4] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,5,6,4,1,3] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,6,3,5,1,4] => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,6,4,1,5,3] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,6,4,5,1,3] => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,6,5,1,3,4] => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,6,5,1,4,3] => [2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,6,5,3,1,4] => [2,5,3,1,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[2,6,5,4,1,3] => [2,5,4,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,1,5,2,4,6] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,1,5,2,6,4] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,1,5,6,2,4] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,1,6,5,2,4] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,2,5,1,4,6] => [3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,2,5,1,6,4] => [3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,2,5,6,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,2,6,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,5,1,2,4,6] => [3,5,1,2,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,5,1,2,6,4] => [3,5,1,2,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2

Description

The determinant of the distance matrix of a connected graph.

Matching statistic: St000264

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [1,2] => [1,2] => ([],2)
 => ? = 2 + 1
[1,3,2] => [1,2] => [1,2] => ([],2)
 => ? = 2 + 1
[3,1,2] => [1,2] => [1,2] => ([],2)
 => ? = 2 + 1
[1,2,3,4] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 + 1
[1,2,4,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 + 1
[1,3,2,4] => [1,3,2] => [1,2,3] => ([],3)
 => ? = 2 + 1
[1,3,4,2] => [1,3,2] => [1,2,3] => ([],3)
 => ? = 2 + 1
[1,4,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 + 1
[1,4,3,2] => [1,3,2] => [1,2,3] => ([],3)
 => ? = 2 + 1
[2,1,3,4] => [2,1,3] => [1,2,3] => ([],3)
 => ? = 2 + 1
[2,1,4,3] => [2,1,3] => [1,2,3] => ([],3)
 => ? = 2 + 1
[2,4,1,3] => [2,1,3] => [1,2,3] => ([],3)
 => ? = 2 + 1
[4,1,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 + 1
[4,1,3,2] => [1,3,2] => [1,2,3] => ([],3)
 => ? = 2 + 1
[4,2,1,3] => [2,1,3] => [1,2,3] => ([],3)
 => ? = 2 + 1
[1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,2,4,3,5] => [1,2,4,3] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,2,4,5,3] => [1,2,4,3] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,2,5,4,3] => [1,2,4,3] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,3,2,4,5] => [1,3,2,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,3,2,5,4] => [1,3,2,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,3,4,2,5] => [1,3,4,2] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[1,3,4,5,2] => [1,3,4,2] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[1,3,5,2,4] => [1,3,2,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,3,5,4,2] => [1,3,4,2] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[1,4,2,3,5] => [1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[1,4,2,5,3] => [1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[1,4,3,2,5] => [1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[1,4,3,5,2] => [1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[1,4,5,2,3] => [1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[1,4,5,3,2] => [1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,5,2,4,3] => [1,2,4,3] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,5,3,2,4] => [1,3,2,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[1,5,3,4,2] => [1,3,4,2] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[1,5,4,2,3] => [1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[1,5,4,3,2] => [1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[2,1,3,4,5] => [2,1,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[2,1,3,5,4] => [2,1,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[2,1,4,3,5] => [2,1,4,3] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[2,1,4,5,3] => [2,1,4,3] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[2,1,5,3,4] => [2,1,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 + 1
[2,1,5,4,3] => [2,1,4,3] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[2,3,1,4,5] => [2,3,1,4] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[2,3,1,5,4] => [2,3,1,4] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[2,3,5,1,4] => [2,3,1,4] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[2,4,1,3,5] => [2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[2,4,1,5,3] => [2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 1
[1,5,2,3,4,6] => [1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,5,2,3,6,4] => [1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,5,2,6,3,4] => [1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,5,3,2,4,6] => [1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,5,3,2,6,4] => [1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,5,3,6,2,4] => [1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,5,6,2,3,4] => [1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,5,6,3,2,4] => [1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,6,5,2,3,4] => [1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,6,5,3,2,4] => [1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,5,1,3,4,6] => [2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,5,1,3,6,4] => [2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,5,1,6,3,4] => [2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,5,3,1,4,6] => [2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,5,3,1,6,4] => [2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,5,3,6,1,4] => [2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,5,6,1,3,4] => [2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,5,6,3,1,4] => [2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,6,5,1,3,4] => [2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[2,6,5,3,1,4] => [2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,1,5,2,4,6] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,1,5,2,6,4] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,1,5,6,2,4] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,1,6,5,2,4] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,2,5,1,4,6] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,2,5,1,6,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,2,5,6,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,2,6,5,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,6,1,5,2,4] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[3,6,2,5,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,1,2,3,5,6] => [4,1,2,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,1,2,3,6,5] => [4,1,2,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,1,2,6,3,5] => [4,1,2,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,1,6,2,3,5] => [4,1,2,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,2,1,3,5,6] => [4,2,1,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,2,1,3,6,5] => [4,2,1,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,2,1,6,3,5] => [4,2,1,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,2,6,1,3,5] => [4,2,1,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,6,1,2,3,5] => [4,1,2,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[4,6,2,1,3,5] => [4,2,1,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[6,1,5,2,3,4] => [1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[6,1,5,3,2,4] => [1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[6,2,5,1,3,4] => [2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[6,2,5,3,1,4] => [2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[6,3,1,5,2,4] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[6,3,2,5,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[6,4,1,2,3,5] => [4,1,2,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[6,4,2,1,3,5] => [4,2,1,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 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: St001603

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [1,2] => [2]
 => []
 => ? = 2 - 1
[1,3,2] => [1,2] => [2]
 => []
 => ? = 2 - 1
[3,1,2] => [1,2] => [2]
 => []
 => ? = 2 - 1
[1,2,3,4] => [1,2,3] => [3]
 => []
 => ? = 3 - 1
[1,2,4,3] => [1,2,3] => [3]
 => []
 => ? = 3 - 1
[1,3,2,4] => [1,3,2] => [2,1]
 => [1]
 => ? = 2 - 1
[1,3,4,2] => [1,3,2] => [2,1]
 => [1]
 => ? = 2 - 1
[1,4,2,3] => [1,2,3] => [3]
 => []
 => ? = 3 - 1
[1,4,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? = 2 - 1
[2,1,3,4] => [2,1,3] => [2,1]
 => [1]
 => ? = 2 - 1
[2,1,4,3] => [2,1,3] => [2,1]
 => [1]
 => ? = 2 - 1
[2,4,1,3] => [2,1,3] => [2,1]
 => [1]
 => ? = 2 - 1
[4,1,2,3] => [1,2,3] => [3]
 => []
 => ? = 3 - 1
[4,1,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? = 2 - 1
[4,2,1,3] => [2,1,3] => [2,1]
 => [1]
 => ? = 2 - 1
[1,2,3,4,5] => [1,2,3,4] => [4]
 => []
 => ? = 3 - 1
[1,2,3,5,4] => [1,2,3,4] => [4]
 => []
 => ? = 3 - 1
[1,2,4,3,5] => [1,2,4,3] => [3,1]
 => [1]
 => ? = 3 - 1
[1,2,4,5,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? = 3 - 1
[1,2,5,3,4] => [1,2,3,4] => [4]
 => []
 => ? = 3 - 1
[1,2,5,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? = 3 - 1
[1,3,2,4,5] => [1,3,2,4] => [3,1]
 => [1]
 => ? = 3 - 1
[1,3,2,5,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? = 3 - 1
[1,3,4,2,5] => [1,3,4,2] => [3,1]
 => [1]
 => ? = 2 - 1
[1,3,4,5,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? = 2 - 1
[1,3,5,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? = 3 - 1
[1,3,5,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? = 2 - 1
[1,4,2,3,5] => [1,4,2,3] => [3,1]
 => [1]
 => ? = 2 - 1
[1,4,2,5,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? = 2 - 1
[1,4,3,2,5] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? = 2 - 1
[1,4,3,5,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? = 2 - 1
[1,4,5,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? = 2 - 1
[1,4,5,3,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? = 2 - 1
[1,5,2,3,4] => [1,2,3,4] => [4]
 => []
 => ? = 3 - 1
[1,5,2,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? = 3 - 1
[1,5,3,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? = 3 - 1
[1,5,3,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? = 2 - 1
[1,5,4,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? = 2 - 1
[1,5,4,3,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? = 2 - 1
[2,1,3,4,5] => [2,1,3,4] => [3,1]
 => [1]
 => ? = 3 - 1
[2,1,3,5,4] => [2,1,3,4] => [3,1]
 => [1]
 => ? = 3 - 1
[2,1,4,3,5] => [2,1,4,3] => [2,2]
 => [2]
 => ? = 2 - 1
[2,1,4,5,3] => [2,1,4,3] => [2,2]
 => [2]
 => ? = 2 - 1
[2,1,5,3,4] => [2,1,3,4] => [3,1]
 => [1]
 => ? = 3 - 1
[2,1,5,4,3] => [2,1,4,3] => [2,2]
 => [2]
 => ? = 2 - 1
[2,3,1,4,5] => [2,3,1,4] => [3,1]
 => [1]
 => ? = 2 - 1
[2,3,1,5,4] => [2,3,1,4] => [3,1]
 => [1]
 => ? = 2 - 1
[2,3,5,1,4] => [2,3,1,4] => [3,1]
 => [1]
 => ? = 2 - 1
[2,4,1,3,5] => [2,4,1,3] => [2,2]
 => [2]
 => ? = 2 - 1
[2,4,1,5,3] => [2,4,1,3] => [2,2]
 => [2]
 => ? = 2 - 1
[1,5,4,3,2,6] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[1,5,4,3,6,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[1,5,4,6,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[1,5,6,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[1,6,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[2,1,5,4,3,6] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,1,5,4,6,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,1,5,6,4,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,1,6,5,4,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,5,1,4,3,6] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,5,1,4,6,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,5,1,6,4,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,5,4,1,3,6] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,5,4,1,6,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,5,4,6,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,5,6,1,4,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,5,6,4,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,6,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,6,5,1,4,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[2,6,5,4,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,2,1,5,4,6] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,2,1,5,6,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,2,1,6,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,2,5,1,4,6] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,2,5,1,6,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,2,5,6,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,2,6,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,2,6,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,5,2,1,4,6] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,5,2,1,6,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,5,2,6,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,5,6,2,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,6,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,6,2,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[3,6,5,2,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[4,3,2,1,5,6] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[4,3,2,1,6,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[4,3,2,6,1,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[4,3,6,2,1,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[4,6,3,2,1,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[6,1,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
[6,2,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[6,2,5,1,4,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[6,2,5,4,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[6,3,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[6,3,2,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[6,3,5,2,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
[6,4,3,2,1,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1

Description

The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. Two colourings are considered equal, if they are obtained by an action of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.

Matching statistic: St001604

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [1,2] => [2]
 => []
 => ? = 2 - 2
[1,3,2] => [1,2] => [2]
 => []
 => ? = 2 - 2
[3,1,2] => [1,2] => [2]
 => []
 => ? = 2 - 2
[1,2,3,4] => [1,2,3] => [3]
 => []
 => ? = 3 - 2
[1,2,4,3] => [1,2,3] => [3]
 => []
 => ? = 3 - 2
[1,3,2,4] => [1,3,2] => [2,1]
 => [1]
 => ? = 2 - 2
[1,3,4,2] => [1,3,2] => [2,1]
 => [1]
 => ? = 2 - 2
[1,4,2,3] => [1,2,3] => [3]
 => []
 => ? = 3 - 2
[1,4,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? = 2 - 2
[2,1,3,4] => [2,1,3] => [2,1]
 => [1]
 => ? = 2 - 2
[2,1,4,3] => [2,1,3] => [2,1]
 => [1]
 => ? = 2 - 2
[2,4,1,3] => [2,1,3] => [2,1]
 => [1]
 => ? = 2 - 2
[4,1,2,3] => [1,2,3] => [3]
 => []
 => ? = 3 - 2
[4,1,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? = 2 - 2
[4,2,1,3] => [2,1,3] => [2,1]
 => [1]
 => ? = 2 - 2
[1,2,3,4,5] => [1,2,3,4] => [4]
 => []
 => ? = 3 - 2
[1,2,3,5,4] => [1,2,3,4] => [4]
 => []
 => ? = 3 - 2
[1,2,4,3,5] => [1,2,4,3] => [3,1]
 => [1]
 => ? = 3 - 2
[1,2,4,5,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? = 3 - 2
[1,2,5,3,4] => [1,2,3,4] => [4]
 => []
 => ? = 3 - 2
[1,2,5,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? = 3 - 2
[1,3,2,4,5] => [1,3,2,4] => [3,1]
 => [1]
 => ? = 3 - 2
[1,3,2,5,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? = 3 - 2
[1,3,4,2,5] => [1,3,4,2] => [3,1]
 => [1]
 => ? = 2 - 2
[1,3,4,5,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? = 2 - 2
[1,3,5,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? = 3 - 2
[1,3,5,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? = 2 - 2
[1,4,2,3,5] => [1,4,2,3] => [3,1]
 => [1]
 => ? = 2 - 2
[1,4,2,5,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? = 2 - 2
[1,4,3,2,5] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? = 2 - 2
[1,4,3,5,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? = 2 - 2
[1,4,5,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? = 2 - 2
[1,4,5,3,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? = 2 - 2
[1,5,2,3,4] => [1,2,3,4] => [4]
 => []
 => ? = 3 - 2
[1,5,2,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? = 3 - 2
[1,5,3,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? = 3 - 2
[1,5,3,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? = 2 - 2
[1,5,4,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? = 2 - 2
[1,5,4,3,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? = 2 - 2
[2,1,3,4,5] => [2,1,3,4] => [3,1]
 => [1]
 => ? = 3 - 2
[2,1,3,5,4] => [2,1,3,4] => [3,1]
 => [1]
 => ? = 3 - 2
[2,1,4,3,5] => [2,1,4,3] => [2,2]
 => [2]
 => ? = 2 - 2
[2,1,4,5,3] => [2,1,4,3] => [2,2]
 => [2]
 => ? = 2 - 2
[2,1,5,3,4] => [2,1,3,4] => [3,1]
 => [1]
 => ? = 3 - 2
[2,1,5,4,3] => [2,1,4,3] => [2,2]
 => [2]
 => ? = 2 - 2
[2,3,1,4,5] => [2,3,1,4] => [3,1]
 => [1]
 => ? = 2 - 2
[2,3,1,5,4] => [2,3,1,4] => [3,1]
 => [1]
 => ? = 2 - 2
[2,3,5,1,4] => [2,3,1,4] => [3,1]
 => [1]
 => ? = 2 - 2
[2,4,1,3,5] => [2,4,1,3] => [2,2]
 => [2]
 => ? = 2 - 2
[2,4,1,5,3] => [2,4,1,3] => [2,2]
 => [2]
 => ? = 2 - 2
[1,5,4,3,2,6] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[1,5,4,3,6,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[1,5,4,6,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[1,5,6,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[1,6,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[2,1,5,4,3,6] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,1,5,4,6,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,1,5,6,4,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,1,6,5,4,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,5,1,4,3,6] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,5,1,4,6,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,5,1,6,4,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,5,4,1,3,6] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,5,4,1,6,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,5,4,6,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,5,6,1,4,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,5,6,4,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,6,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,6,5,1,4,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[2,6,5,4,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,2,1,5,4,6] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,2,1,5,6,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,2,1,6,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,2,5,1,4,6] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,2,5,1,6,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,2,5,6,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,2,6,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,2,6,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,5,2,1,4,6] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,5,2,1,6,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,5,2,6,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,5,6,2,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,6,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,6,2,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[3,6,5,2,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[4,3,2,1,5,6] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[4,3,2,1,6,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[4,3,2,6,1,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[4,3,6,2,1,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[4,6,3,2,1,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[6,1,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2
[6,2,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[6,2,5,1,4,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[6,2,5,4,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[6,3,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[6,3,2,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[6,3,5,2,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 0 = 2 - 2
[6,4,3,2,1,5] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0 = 2 - 2

Description

The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.

Matching statistic: St001630

Mapping

Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 50%

Values

[1,2,3] => [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ? = 2
[1,3,2] => [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[3,1,2] => [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ? = 2
[1,2,3,4] => [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1)],2)
 => ? = 3
[1,2,4,3] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1)],2)
 => ? = 3
[1,3,2,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1)],2)
 => ? = 2
[1,3,4,2] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,2,3] => [3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1)],2)
 => ? = 3
[1,4,3,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[2,1,3,4] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1)],2)
 => ? = 2
[2,1,4,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1)],2)
 => ? = 2
[2,4,1,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1)],2)
 => ? = 2
[4,1,2,3] => [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ([],1)
 => ? = 3
[4,1,3,2] => [4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1)],2)
 => ? = 2
[4,2,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,2,3,4,5] => [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
 => ([(0,1)],2)
 => ? = 3
[1,2,3,5,4] => [2,3,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
 => ([(0,1)],2)
 => ? = 3
[1,2,4,3,5] => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ([(0,1)],2)
 => ? = 3
[1,2,4,5,3] => [2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 3
[1,2,5,3,4] => [2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 3
[1,2,5,4,3] => [2,5,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(0,1)],2)
 => ? = 3
[1,3,2,4,5] => [3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
 => ([(0,1)],2)
 => ? = 3
[1,3,2,5,4] => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ([(0,1)],2)
 => ? = 3
[1,3,4,2,5] => [4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 2
[1,3,4,5,2] => [5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,5,2,4] => [4,2,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
 => ([(0,1)],2)
 => ? = 3
[1,3,5,4,2] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,2,3,5] => [3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 2
[1,4,2,5,3] => [3,5,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
 => ([(0,1)],2)
 => ? = 2
[1,4,3,2,5] => [4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(0,1)],2)
 => ? = 2
[1,4,3,5,2] => [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,5,2,3] => [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
 => ([(0,1)],2)
 => ? = 2
[1,4,5,3,2] => [5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,5,2,3,4] => [3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ([(0,1)],2)
 => ? = 3
[1,5,2,4,3] => [3,5,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1)],2)
 => ? = 3
[1,5,3,2,4] => [4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1)],2)
 => ? = 3
[1,5,3,4,2] => [5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,5,4,2,3] => [4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
 => ([(0,1)],2)
 => ? = 2
[1,5,4,3,2] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[2,1,3,4,5] => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(0,1)],2)
 => ? = 3
[2,1,3,5,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 3
[2,1,4,3,5] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 2
[2,1,4,5,3] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ([(0,1)],2)
 => ? = 2
[2,1,5,3,4] => [1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
 => ([(0,1)],2)
 => ? = 3
[2,1,5,4,3] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
 => ([(0,1)],2)
 => ? = 2
[2,3,1,4,5] => [1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1)],2)
 => ? = 2
[2,3,1,5,4] => [1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ([(0,1)],2)
 => ? = 2
[2,3,5,1,4] => [1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1)],2)
 => ? = 2
[2,4,1,3,5] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
 => ([(0,1)],2)
 => ? = 2
[2,4,1,5,3] => [1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 2
[2,4,5,1,3] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(0,1)],2)
 => ? = 2
[2,5,1,3,4] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ([(0,1)],2)
 => ? = 3
[2,5,1,4,3] => [1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
 => ([(0,1)],2)
 => ? = 2
[2,5,3,1,4] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
 => ([(0,1)],2)
 => ? = 2
[2,5,4,1,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 2
[3,1,2,4,5] => [3,1,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
 => ([],1)
 => ? = 2
[3,1,2,5,4] => [3,1,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
 => ([],1)
 => ? = 2
[3,1,5,2,4] => [4,1,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
 => ([],1)
 => ? = 2
[3,2,1,4,5] => [2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
 => ([],1)
 => ? = 2
[3,2,1,5,4] => [2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
 => ([],1)
 => ? = 2
[3,5,2,1,4] => [3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
[5,2,4,1,3] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
[5,3,1,2,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
[1,3,4,5,6,2] => [6,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,4,6,5,2] => [6,2,3,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,5,4,6,2] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,5,6,4,2] => [6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,6,4,5,2] => [6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,6,5,4,2] => [6,2,5,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,3,5,6,2] => [6,3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,3,6,5,2] => [6,3,2,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,5,3,6,2] => [6,4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,5,6,3,2] => [6,5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,6,3,5,2] => [6,4,2,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,4,6,5,3,2] => [6,5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,5,3,4,6,2] => [6,3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,5,3,6,4,2] => [6,3,5,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,5,4,3,6,2] => [6,4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,5,4,6,3,2] => [6,5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,5,6,3,4,2] => [6,4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,5,6,4,3,2] => [6,5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,6,3,4,5,2] => [6,3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,6,4,3,5,2] => [6,4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,6,4,5,3,2] => [6,5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,6,5,3,4,2] => [6,4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2

Description

The global dimension of the incidence algebra of the lattice over the rational numbers.

The following 9 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000454The largest eigenvalue of a graph if it is integral. St000422The energy of a graph, if it is integral. 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. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices.