Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000244
(load all 6 compositions to match this statistic)
Mapping
St000244: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 2
([],3)
 => 6
([(1,2)],3)
 => 2
([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => 6
([],4)
 => 24
([(2,3)],4)
 => 4
([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 6
([(0,3),(1,2)],4)
 => 8
([(0,3),(1,2),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => 6
([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => 8
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 24
([],5)
 => 120
([(3,4)],5)
 => 12
([(2,4),(3,4)],5)
 => 4
([(1,4),(2,4),(3,4)],5)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => 24
([(1,4),(2,3)],5)
 => 8
([(1,4),(2,3),(3,4)],5)
 => 2
([(0,1),(2,4),(3,4)],5)
 => 4
([(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(1,3),(1,4),(2,3),(2,4)],5)
 => 8
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 12
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => 12
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 8
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 10
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 24
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 8
Description
The cardinality of the automorphism group of a graph.
Matching statistic: St000511
(load all 2 compositions to match this statistic)
Mapping
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
St000511: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 31%●distinct values known / distinct values provided: 29%
Values
([],1)
 => [1]
 => []
 => ?
 => ? = 1
([],2)
 => [1,1]
 => [1]
 => [1]
 => 2
([(0,1)],2)
 => [2]
 => []
 => ?
 => ? = 2
([],3)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(1,2)],3)
 => [2,1]
 => [1]
 => [1]
 => 2
([(0,2),(1,2)],3)
 => [3]
 => []
 => ?
 => ? ∊ {6,6}
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ?
 => ? ∊ {6,6}
([],4)
 => [1,1,1,1]
 => [1,1,1]
 => [2,1]
 => 4
([(2,3)],4)
 => [2,1,1]
 => [1,1]
 => [2]
 => 2
([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => [1]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ?
 => ? ∊ {6,6,8,8,24,24}
([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => [1,1]
 => 4
([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ?
 => ? ∊ {6,6,8,8,24,24}
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => [1]
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ?
 => ? ∊ {6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ?
 => ? ∊ {6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ?
 => ? ∊ {6,6,8,8,24,24}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ?
 => ? ∊ {6,6,8,8,24,24}
([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 2
([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [2,1]
 => 4
([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => [1,1,1]
 => 8
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 2
([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => [1,1]
 => 4
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => [1,1]
 => 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? ∊ {2,2,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [4,1]
 => 4
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 2
([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [2,1]
 => 4
([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [2,1,1]
 => 8
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(1,2),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => [1,1,1]
 => 8
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [2,1]
 => 4
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 4
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => [3,3]
 => [3]
 => [3]
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [2,2]
 => [1,1,1,1]
 => 16
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 4
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => [1,1,1]
 => 8
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 4
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5,1]
 => [1]
 => [1]
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
Description
The number of invariant subsets when acting with a permutation of given cycle type.
Matching statistic: St000514
(load all 3 compositions to match this statistic)
Mapping
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000514: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 30%●distinct values known / distinct values provided: 29%
Values
([],1)
 => []
 => ?
 => ?
 => ? = 1
([],2)
 => []
 => ?
 => ?
 => ? ∊ {2,2}
([(0,1)],2)
 => [1]
 => []
 => []
 => ? ∊ {2,2}
([],3)
 => []
 => ?
 => ?
 => ? ∊ {2,2,6,6}
([(1,2)],3)
 => [1]
 => []
 => []
 => ? ∊ {2,2,6,6}
([(0,2),(1,2)],3)
 => [1,1]
 => [1]
 => [1]
 => ? ∊ {2,2,6,6}
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => []
 => ? ∊ {2,2,6,6}
([],4)
 => []
 => ?
 => ?
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([(2,3)],4)
 => [1]
 => []
 => []
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([(1,3),(2,3)],4)
 => [1,1]
 => [1]
 => [1]
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([(0,3),(1,3),(2,3)],4)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => [1]
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([(0,3),(1,2),(2,3)],4)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => []
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => [1]
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => []
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => []
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => []
 => ? ∊ {2,4,4,6,6,8,8,24,24}
([],5)
 => []
 => ?
 => ?
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(3,4)],5)
 => [1]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(2,4),(3,4)],5)
 => [1,1]
 => [1]
 => [1]
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,4),(3,4)],5)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => [1]
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3),(3,4)],5)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(0,1),(2,4),(3,4)],5)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,3),(3,4)],5)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => [1]
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [1]
 => [1]
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => [1]
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [3]
 => [1,1,1]
 => 8
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [1]
 => [1]
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6,1]
 => [1]
 => [1]
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [8]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [9]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [10]
 => []
 => []
 => ? ∊ {2,2,4,4,4,4,4,4,6,6,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([],6)
 => []
 => ?
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(4,5)],6)
 => [1]
 => []
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(3,5),(4,5)],6)
 => [1,1]
 => [1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,5),(3,5),(4,5)],6)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 4
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,5),(3,4),(4,5)],6)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(1,2),(3,5),(4,5)],6)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,5),(2,5),(3,4),(4,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 4
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4]
 => []
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,5),(2,4),(3,4)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 4
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 4
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 8
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,3,1]
 => [3,1]
 => [2,1,1]
 => 16
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 4
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,3]
 => [3]
 => [1,1,1]
 => 8
Description
The number of invariant simple graphs when acting with a permutation of given cycle type.
Matching statistic: St001630
(load all 2 compositions to match this statistic)
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 14% ●values known / values provided: 18%●distinct values known / distinct values provided: 14%
Values
([],1)
 => ([],1)
 => ([],1)
 => ? = 1
([],2)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2}
([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2}
([],3)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,6,6}
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,6,6}
([(0,2),(1,2)],3)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,6,6}
([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,6,6}
([],4)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2)],4)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(2,3),(2,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([],6)
 => ([],1)
 => ([],1)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(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.
Matching statistic: St001878
(load all 2 compositions to match this statistic)
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 14% ●values known / values provided: 18%●distinct values known / distinct values provided: 14%
Values
([],1)
 => ([],1)
 => ([],1)
 => ? = 1
([],2)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2}
([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2}
([],3)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,6,6}
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,6,6}
([(0,2),(1,2)],3)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,6,6}
([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,6,6}
([],4)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2)],4)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(2,3),(2,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([],6)
 => ([],1)
 => ([],1)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St001060
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 13%●distinct values known / distinct values provided: 7%
Values
([],1)
 => ([],1)
 => ([],1)
 => ? = 1
([],2)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2}
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2}
([],3)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,6,6}
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,6,6}
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,2,6,6}
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,6,6}
([],4)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,4,4,6,6,8,8,24,24}
([],5)
 => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,4,4,4,4,4,4,6,6,8,8,8,8,10,12,12,12,12,12,12,24,24,120,120}
([],6)
 => ([],6)
 => ([],1)
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,24,24,36,36,48,48,48,48,48,48,48,48,72,72,120,120,720,720}
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
Description
The distinguishing index of a graph. This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism. If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.