- FindStat

Your data matches 17 different statistics following compositions of up to 3 maps.
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Matching statistic: St000912
(load all 2 compositions to match this statistic)

Mapping

St000912: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

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

Description

The number of maximal antichains in a poset.

Matching statistic: St000228

Mapping

Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000228: Integer partitions ⟶ ℤResult quality: 62% ●values known / values provided: 99%●distinct values known / distinct values provided: 62%

Values

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

Description

The size of a partition. This statistic is the constant statistic of the level sets.

Matching statistic: St001622

Mapping

Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001622: Lattices ⟶ ℤResult quality: 56% ●values known / values provided: 95%●distinct values known / distinct values provided: 56%

Values

([],1)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([],3)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,1),(0,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([],4)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,3),(3,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 4
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([],5)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => 5
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => 2
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 4
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 4
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,8),(2,13),(3,11),(4,9),(5,10),(6,3),(6,10),(7,4),(7,12),(8,5),(8,6),(9,13),(10,7),(10,11),(11,12),(12,2),(12,9),(13,1)],14)
 => ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
 => ? = 9
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
 => ? = 8
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
 => ? = 8
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ?
 => ? = 9
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
 => ? = 9
([(0,6),(1,5),(2,5),(2,6),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
 => ? = 8
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
 => ? = 8
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
 => ? = 8
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,8),(2,13),(3,11),(4,9),(5,10),(6,3),(6,10),(7,4),(7,12),(8,5),(8,6),(9,13),(10,7),(10,11),(11,12),(12,2),(12,9),(13,1)],14)
 => ? = 8
([(0,6),(1,6),(2,3),(3,5),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
 => ? = 9
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
 => ? = 8
([(0,6),(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
 => ? = 8
([(0,6),(1,6),(2,3),(4,5),(6,4)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
 => ? = 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ?
 => ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(2,10),(3,11),(4,9),(5,4),(5,11),(6,1),(7,8),(8,3),(8,5),(9,10),(10,6),(11,2),(11,9)],12)
 => ? = 8
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(2,10),(3,11),(4,9),(5,4),(5,11),(6,1),(7,8),(8,3),(8,5),(9,10),(10,6),(11,2),(11,9)],12)
 => ? = 8
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,8),(2,13),(3,11),(4,9),(5,10),(6,3),(6,10),(7,4),(7,12),(8,5),(8,6),(9,13),(10,7),(10,11),(11,12),(12,2),(12,9),(13,1)],14)
 => ? = 8
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ?
 => ? = 9
([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,8),(1,10),(2,11),(4,9),(5,3),(6,4),(6,11),(7,5),(8,2),(8,6),(9,10),(10,7),(11,1),(11,9)],12)
 => ? = 8
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ?
 => ? = 10
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,9),(2,15),(3,14),(4,11),(5,13),(6,7),(6,14),(7,5),(7,10),(8,1),(9,3),(9,6),(10,13),(10,15),(11,8),(12,11),(13,12),(14,2),(14,10),(15,4),(15,12)],16)
 => ? = 9
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ?
 => ? = 9
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ?
 => ? = 10
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ?
 => ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,8),(2,9),(3,9),(4,10),(5,10),(6,1),(7,4),(7,5),(8,2),(8,3),(9,7),(10,6)],11)
 => ? = 8
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
 => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
 => ?
 => ?
 => ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
 => ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
 => ?
 => ?
 => ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
 => ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
 => ?
 => ?
 => ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ?
 => ? = 10
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,6),(1,10),(2,10),(4,9),(5,9),(6,7),(7,4),(7,5),(8,1),(8,2),(9,8),(10,3)],11)
 => ? = 8
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
 => ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
 => ?
 => ?
 => ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
 => ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
 => ?
 => ?
 => ? = 12
([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,7),(7,2),(7,3),(8,4),(8,5),(9,6),(10,1)],11)
 => ? = 8
([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,8),(1,10),(2,11),(4,9),(5,3),(6,4),(6,11),(7,5),(8,2),(8,6),(9,10),(10,7),(11,1),(11,9)],12)
 => ? = 8
([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,9),(2,15),(3,14),(4,11),(5,13),(6,7),(6,14),(7,5),(7,10),(8,1),(9,3),(9,6),(10,13),(10,15),(11,8),(12,11),(13,12),(14,2),(14,10),(15,4),(15,12)],16)
 => ? = 9
([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,9),(8,9),(9,10)],11)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ?
 => ? = 11
([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ?
 => ? = 10
([(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)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ?
 => ? = 8
([(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)
 => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
 => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
 => ?
 => ? = 9
([(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)
 => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
 => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
 => ?
 => ? = 10
([(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)
 => ([(0,3),(0,4),(0,5),(2,9),(3,8),(3,10),(4,7),(4,10),(5,7),(5,8),(6,1),(7,11),(8,11),(9,6),(10,2),(10,11),(11,9)],12)
 => ([(0,3),(0,4),(0,5),(2,9),(3,8),(3,10),(4,7),(4,10),(5,7),(5,8),(6,1),(7,11),(8,11),(9,6),(10,2),(10,11),(11,9)],12)
 => ?
 => ? = 12
([(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)
 => ([(0,5),(0,6),(2,9),(3,8),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8),(7,9),(8,10),(9,10),(10,4)],11)
 => ([(0,5),(0,6),(2,9),(3,8),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8),(7,9),(8,10),(9,10),(10,4)],11)
 => ?
 => ? = 11
([(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)
 => ([(0,3),(0,6),(2,10),(3,7),(4,5),(4,9),(5,2),(5,8),(6,4),(6,7),(7,9),(8,10),(9,8),(10,1)],11)
 => ([(0,3),(0,6),(2,10),(3,7),(4,5),(4,9),(5,2),(5,8),(6,4),(6,7),(7,9),(8,10),(9,8),(10,1)],11)
 => ?
 => ? = 11
([(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)
 => ([(0,3),(0,4),(0,5),(2,11),(3,7),(3,8),(4,8),(4,9),(5,7),(5,9),(6,2),(6,10),(7,12),(8,12),(9,6),(9,12),(10,11),(11,1),(12,10)],13)
 => ([(0,3),(0,4),(0,5),(2,11),(3,7),(3,8),(4,8),(4,9),(5,7),(5,9),(6,2),(6,10),(7,12),(8,12),(9,6),(9,12),(10,11),(11,1),(12,10)],13)
 => ?
 => ? = 13
([(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)
 => ([(0,4),(0,5),(0,6),(1,11),(3,10),(3,12),(4,7),(4,8),(5,7),(5,9),(6,3),(6,8),(6,9),(7,14),(8,12),(8,14),(9,10),(9,14),(10,13),(11,2),(12,1),(12,13),(13,11),(14,13)],15)
 => ([(0,4),(0,5),(0,6),(1,11),(3,10),(3,12),(4,7),(4,8),(5,7),(5,9),(6,3),(6,8),(6,9),(7,14),(8,12),(8,14),(9,10),(9,14),(10,13),(11,2),(12,1),(12,13),(13,11),(14,13)],15)
 => ?
 => ? = 15
([(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)
 => ([(0,5),(0,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,7),(6,4),(6,7),(7,8),(7,10),(8,11),(9,12),(10,9),(10,11),(11,12),(12,1)],13)
 => ([(0,5),(0,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,7),(6,4),(6,7),(7,8),(7,10),(8,11),(9,12),(10,9),(10,11),(11,12),(12,1)],13)
 => ?
 => ? = 13
([(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)
 => ([(0,4),(0,5),(0,6),(2,11),(3,7),(3,8),(4,10),(4,13),(5,10),(5,12),(6,3),(6,12),(6,13),(7,15),(8,15),(9,1),(10,2),(10,14),(11,9),(12,7),(12,14),(13,8),(13,14),(14,11),(14,15),(15,9)],16)
 => ([(0,4),(0,5),(0,6),(2,11),(3,7),(3,8),(4,10),(4,13),(5,10),(5,12),(6,3),(6,12),(6,13),(7,15),(8,15),(9,1),(10,2),(10,14),(11,9),(12,7),(12,14),(13,8),(13,14),(14,11),(14,15),(15,9)],16)
 => ?
 => ? = 16
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(5,7)],8)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
 => ? = 9
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
 => ? = 8

Description

The number of join-irreducible elements of a lattice. An element

$j$ of a lattice

$L$ is '''join irreducible''' if it is not the least element and if

$j=x\vee y$ , then

$j\in\{x,y\}$ for all

$x,y\in L$ .

Matching statistic: St001342

Mapping

Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001342: Graphs ⟶ ℤResult quality: 44% ●values known / values provided: 95%●distinct values known / distinct values provided: 44%

Values

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

Description

The number of vertices in the center of a graph. The center of a graph is the set of vertices whose maximal distance to any other vertex is minimal. In particular, if the graph is disconnected, all vertices are in the certer.

Matching statistic: St000987

Mapping

Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000987: Graphs ⟶ ℤResult quality: 44% ●values known / values provided: 95%●distinct values known / distinct values provided: 44%

Values

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

Description

The number of positive eigenvalues of the Laplacian matrix of the graph. This is the number of vertices minus the number of connected components of the graph.

Matching statistic: St001717
(load all 2 compositions to match this statistic)

Mapping

Mp00125: Posets —dual poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001717: Posets ⟶ ℤResult quality: 44% ●values known / values provided: 92%●distinct values known / distinct values provided: 44%

Values

([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,2),(2,3)],4)
 => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,3),(2,3)],4)
 => ([(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(3,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(2,3),(3,4)],5)
 => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(2,4),(3,4)],5)
 => ([(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)
 => ([(0,4),(1,3),(1,5),(2,6),(3,6),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ? = 9
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7)
 => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7)
 => ([(0,5),(1,4),(4,2),(4,6),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
 => ([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)
 => ([(0,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7)
 => ([(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(4,2)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(2,5),(2,6),(3,4)],7)
 => ([(0,5),(1,4),(1,6),(2,3),(2,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7)
 => ([(0,5),(1,3),(1,6),(4,2),(4,6),(5,4)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
 => ([(0,4),(0,5),(3,2),(3,6),(4,3),(5,1),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(0,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,5),(1,2),(1,3),(1,6),(4,6),(5,4)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7)
 => ([(0,4),(1,5),(1,6),(4,6),(5,2),(5,3)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7)
 => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(3,5),(6,4)],7)
 => ([(0,6),(1,5),(5,4),(6,2),(6,3)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,6),(1,3),(1,4),(5,2),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,6),(2,3),(4,5),(6,4)],7)
 => ([(0,4),(1,5),(5,6),(6,2),(6,3)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7)
 => ([(0,5),(0,6),(1,3),(1,6),(3,4),(4,2),(4,5)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7)
 => ([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
 => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)
 => ([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(1,3),(2,4),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)
 => ([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
 => ([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 8
([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)
 => ([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 8
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)
 => ([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7)
 => ([(0,3),(1,4),(1,5),(1,6),(3,5),(3,6),(4,2)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7)
 => ([(0,6),(1,3),(2,4),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7

Description

The largest size of an interval in a poset.

Matching statistic: St001300
(load all 2 compositions to match this statistic)

Mapping

Mp00125: Posets —dual poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001300: Posets ⟶ ℤResult quality: 44% ●values known / values provided: 92%●distinct values known / distinct values provided: 44%

Values

([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(1,2),(2,3)],4)
 => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(1,3),(2,3)],4)
 => ([(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(3,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 4 = 5 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(2,3),(3,4)],5)
 => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(2,4),(3,4)],5)
 => ([(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8 - 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9 - 1
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8 - 1
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8 - 1
([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)
 => ([(0,4),(1,3),(1,5),(2,6),(3,6),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ? = 9 - 1
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7)
 => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7)
 => ([(0,5),(1,4),(4,2),(4,6),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9 - 1
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
 => ([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)
 => ([(0,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7)
 => ([(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(4,2)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,5),(2,5),(2,6),(3,4)],7)
 => ([(0,5),(1,4),(1,6),(2,3),(2,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8 - 1
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8 - 1
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7)
 => ([(0,5),(1,3),(1,6),(4,2),(4,6),(5,4)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8 - 1
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
 => ([(0,4),(0,5),(3,2),(3,6),(4,3),(5,1),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(0,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,5),(1,2),(1,3),(1,6),(4,6),(5,4)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7)
 => ([(0,4),(1,5),(1,6),(4,6),(5,2),(5,3)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8 - 1
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7)
 => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,6),(2,3),(3,5),(6,4)],7)
 => ([(0,6),(1,5),(5,4),(6,2),(6,3)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9 - 1
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,6),(1,3),(1,4),(5,2),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8 - 1
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,6),(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8 - 1
([(0,6),(1,6),(2,3),(4,5),(6,4)],7)
 => ([(0,4),(1,5),(5,6),(6,2),(6,3)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8 - 1
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7)
 => ([(0,5),(0,6),(1,3),(1,6),(3,4),(4,2),(4,5)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7)
 => ([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
 => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)
 => ([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(1,3),(2,4),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)
 => ([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
 => ([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 10 - 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 8 - 1
([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)
 => ([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 8 - 1
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)
 => ([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7)
 => ([(0,3),(1,4),(1,5),(1,6),(3,5),(3,6),(4,2)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8 - 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7 - 1
([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7)
 => ([(0,6),(1,3),(2,4),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7 - 1

Description

The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset.

Matching statistic: St000656
(load all 2 compositions to match this statistic)

Mapping

Mp00125: Posets —dual poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000656: Posets ⟶ ℤResult quality: 38% ●values known / values provided: 91%●distinct values known / distinct values provided: 38%

Values

([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => ? = 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => ? = 1
([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => ? = 1
([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,2),(2,3)],4)
 => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,3),(2,3)],4)
 => ([(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(3,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => ? = 1
([(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(2,3),(3,4)],5)
 => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(2,4),(3,4)],5)
 => ([(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => ? = 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([],7)
 => ([],7)
 => ([],1)
 => ([],1)
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)
 => ([(0,4),(1,3),(1,5),(2,6),(3,6),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ? = 9
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7)
 => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7)
 => ([(0,5),(1,4),(4,2),(4,6),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
 => ([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)
 => ([(0,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7)
 => ([(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(4,2)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(2,5),(2,6),(3,4)],7)
 => ([(0,5),(1,4),(1,6),(2,3),(2,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7)
 => ([(0,5),(1,3),(1,6),(4,2),(4,6),(5,4)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
 => ([(0,4),(0,5),(3,2),(3,6),(4,3),(5,1),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(0,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,5),(1,2),(1,3),(1,6),(4,6),(5,4)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7)
 => ([(0,4),(1,5),(1,6),(4,6),(5,2),(5,3)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7)
 => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(3,5),(6,4)],7)
 => ([(0,6),(1,5),(5,4),(6,2),(6,3)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,6),(1,3),(1,4),(5,2),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,6),(2,3),(4,5),(6,4)],7)
 => ([(0,4),(1,5),(5,6),(6,2),(6,3)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7)
 => ([(0,5),(0,6),(1,3),(1,6),(3,4),(4,2),(4,5)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7)
 => ([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
 => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)
 => ([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(1,3),(2,4),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)
 => ([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
 => ([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 10

Description

The number of cuts of a poset. A cut is a subset

$A$ of the poset such that the set of lower bounds of the set of upper bounds of

$A$ is exactly

$A$ .

Matching statistic: St001304
(load all 4 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001304: Graphs ⟶ ℤResult quality: 62% ●values known / values provided: 91%●distinct values known / distinct values provided: 62%

Values

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

Description

The number of maximally independent sets of vertices of a graph. An '''independent set''' of vertices of a graph is a set of vertices no two of which are adjacent. If a set of vertices is independent then so is every subset. This statistic counts the number of maximally independent sets of vertices.

Matching statistic: St000189
(load all 2 compositions to match this statistic)

Mapping

Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000189: Posets ⟶ ℤResult quality: 38% ●values known / values provided: 90%●distinct values known / distinct values provided: 38%

Values

([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],4)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(3,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([],5)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 7
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ? = 9
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,5),(2,5),(2,6),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,6),(2,3),(3,5),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 9
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,6),(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(0,6),(1,6),(2,3),(4,5),(6,4)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 8
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 7
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 7
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ? = 7
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 8
([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 7
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 8

Description

The number of elements in the poset.

The following 7 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St000010The length of the partition. St000147The largest part of an integer partition. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001875The number of simple modules with projective dimension at most 1. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001820The size of the image of the pop stack sorting operator.