Processing math: 100%

Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000180
(load all 2 compositions to match this statistic)
Mapping
St000180: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 2
([],2)
 => 3
([(0,1)],2)
 => 4
([],3)
 => 4
([(1,2)],3)
 => 5
([(0,1),(0,2)],3)
 => 6
([(0,2),(2,1)],3)
 => 8
([(0,2),(1,2)],3)
 => 6
([],4)
 => 5
([(2,3)],4)
 => 6
([(1,2),(1,3)],4)
 => 7
([(0,1),(0,2),(0,3)],4)
 => 8
([(0,2),(0,3),(3,1)],4)
 => 10
([(0,1),(0,2),(1,3),(2,3)],4)
 => 12
([(1,2),(2,3)],4)
 => 9
([(0,3),(3,1),(3,2)],4)
 => 12
([(1,3),(2,3)],4)
 => 7
([(0,3),(1,3),(3,2)],4)
 => 12
([(0,3),(1,3),(2,3)],4)
 => 8
([(0,3),(1,2)],4)
 => 7
([(0,3),(1,2),(1,3)],4)
 => 8
([(0,2),(0,3),(1,2),(1,3)],4)
 => 9
([(0,3),(2,1),(3,2)],4)
 => 16
([(0,3),(1,2),(2,3)],4)
 => 10
([],5)
 => 6
([(3,4)],5)
 => 7
([(2,3),(2,4)],5)
 => 8
([(1,2),(1,3),(1,4)],5)
 => 9
([(0,1),(0,2),(0,3),(0,4)],5)
 => 10
([(0,2),(0,3),(0,4),(4,1)],5)
 => 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 14
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 16
([(1,3),(1,4),(4,2)],5)
 => 11
([(0,3),(0,4),(4,1),(4,2)],5)
 => 14
([(1,2),(1,3),(2,4),(3,4)],5)
 => 13
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 24
([(0,3),(0,4),(3,2),(4,1)],5)
 => 14
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 16
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 18
([(2,3),(3,4)],5)
 => 10
([(1,4),(4,2),(4,3)],5)
 => 13
([(0,4),(4,1),(4,2),(4,3)],5)
 => 16
([(2,4),(3,4)],5)
 => 8
([(1,4),(2,4),(4,3)],5)
 => 13
([(0,4),(1,4),(4,2),(4,3)],5)
 => 18
([(1,4),(2,4),(3,4)],5)
 => 9
([(0,4),(1,4),(2,4),(4,3)],5)
 => 16
([(0,4),(1,4),(2,4),(3,4)],5)
 => 10
([(0,4),(1,4),(2,3)],5)
 => 9
([(0,4),(1,3),(2,3),(2,4)],5)
 => 10
Description
The number of chains of a poset.
Matching statistic: St000300
(load all 2 compositions to match this statistic)
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
St000300: Graphs ⟶ ℤResult quality: 64% ●values known / values provided: 77%●distinct values known / distinct values provided: 64%
Values
([],1)
 => ([],1)
 => 2
([],2)
 => ([(0,1)],2)
 => 3
([(0,1)],2)
 => ([],2)
 => 4
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 4
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 5
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => 6
([(0,2),(2,1)],3)
 => ([],3)
 => 8
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 6
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 5
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 6
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 7
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 8
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => 10
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 12
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 9
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => 12
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 7
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => 12
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 8
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 7
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 8
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 9
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 16
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 10
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 7
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 8
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 9
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 16
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 11
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 13
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 24
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 14
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 16
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => 18
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 13
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 16
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 8
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 13
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => 18
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 9
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 16
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 9
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 10
([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9)
 => ([(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 62
([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9)
 => ([(1,8),(2,3),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 46
([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9)
 => ([(1,5),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(6,7),(6,8),(7,8)],9)
 => ? = 38
([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
 => ?
 => ? = 81
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
 => ?
 => ? = 45
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 45
([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 33
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 21
([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8)
 => ?
 => ? = 45
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
 => ?
 => ? = 25
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8)
 => ?
 => ? = 33
([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 17
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
 => ?
 => ? = 21
([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
 => ?
 => ? = 17
([(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 13
([],8)
 => ?
 => ? = 9
([(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
 => ?
 => ? = 63
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
 => ?
 => ? = 45
([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
 => ?
 => ? = 51
([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(6,3),(7,2)],8)
 => ?
 => ? = 63
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
 => ?
 => ? = 31
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
 => ?
 => ? = 33
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
 => ?
 => ? = 37
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
 => ?
 => ? = 45
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
 => ?
 => ? = 51
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
 => ?
 => ? = 41
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
 => ?
 => ? = 37
([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
 => ?
 => ? = 49
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8)
 => ?
 => ? = 63
([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11)
 => ([(1,10),(2,9),(2,10),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
 => ? = 126
([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(1,10),(2,9),(2,10),(3,4),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
 => ? = 94
([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11)
 => ([(1,10),(2,6),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
 => ? = 78
([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(1,7),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)
 => ? = 70
([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,9),(8,9),(9,10)],11)
 => ([(1,8),(1,9),(1,10),(2,3),(2,6),(2,7),(2,8),(2,9),(2,10),(3,4),(3,5),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(9,10)],11)
 => ? = 54
([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11)
 => ([(1,2),(1,4),(1,7),(1,8),(1,10),(2,3),(2,5),(2,6),(2,9),(3,4),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
 => ? = 54
([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13)
 => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,9),(4,10),(4,11),(4,12),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 254
([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13)
 => ([(1,12),(2,11),(2,12),(3,10),(3,11),(3,12),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 190
([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13)
 => ([(1,12),(2,11),(2,12),(3,7),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 158
([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,11),(9,12),(11,9),(12,10)],13)
 => ([(1,12),(2,8),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 142
([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(11,12),(12,10)],13)
 => ([(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 110
([(0,7),(1,7),(2,8),(3,8),(4,11),(5,10),(6,9),(7,10),(8,11),(10,12),(11,12),(12,9)],13)
 => ([(1,12),(2,3),(2,5),(2,8),(2,9),(2,11),(2,12),(3,4),(3,6),(3,7),(3,10),(3,12),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 110
([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13)
 => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,8),(3,9),(3,10),(3,11),(3,12),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
 => ? = 134
([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(10,12),(11,10)],13)
 => ([(1,9),(1,11),(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(10,11),(10,12),(11,12)],13)
 => ? = 102
([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13)
 => ([(1,10),(1,11),(1,12),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(11,12)],13)
 => ? = 86
([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13)
 => ([(1,4),(1,7),(1,9),(1,10),(1,12),(2,4),(2,7),(2,9),(2,10),(2,11),(2,12),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,8),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 86
([(0,10),(1,8),(2,8),(3,7),(4,7),(5,9),(6,9),(7,11),(8,11),(9,10),(10,12),(11,12)],13)
 => ([(1,2),(1,5),(1,10),(1,11),(1,12),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,12),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 70
([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
 => ?
 => ? = 39
([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 31
([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 29
([(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 23
Description
The number of independent sets of vertices of a graph. An independent set of vertices of a graph G is a subset U⊂V(G) such that no two vertices in U are adjacent. This is also the number of vertex covers of G as the map U↦V(G)∖U is a bijection between independent sets of vertices and vertex covers. The size of the largest independent set, also called independence number of G, is [[St000093]]