Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001380
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Mapping
St001380: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 2
[3]
 => 3
[2,1]
 => 3
[1,1,1]
 => 3
[4]
 => 5
[3,1]
 => 5
[2,2]
 => 7
[2,1,1]
 => 5
[1,1,1,1]
 => 5
[5]
 => 8
[4,1]
 => 8
[3,2]
 => 10
[3,1,1]
 => 8
[2,2,1]
 => 10
[2,1,1,1]
 => 8
[1,1,1,1,1]
 => 8
[6]
 => 13
[5,1]
 => 13
[4,2]
 => 17
[4,1,1]
 => 13
[3,3]
 => 22
[3,2,1]
 => 14
[3,1,1,1]
 => 13
[2,2,2]
 => 22
[2,2,1,1]
 => 17
[2,1,1,1,1]
 => 13
[1,1,1,1,1,1]
 => 13
[7]
 => 21
[6,1]
 => 21
[5,2]
 => 27
[5,1,1]
 => 21
[4,3]
 => 32
[4,2,1]
 => 24
[4,1,1,1]
 => 21
[3,3,1]
 => 32
[3,2,2]
 => 32
[3,2,1,1]
 => 24
[3,1,1,1,1]
 => 21
[2,2,2,1]
 => 32
[2,2,1,1,1]
 => 27
[2,1,1,1,1,1]
 => 21
[1,1,1,1,1,1,1]
 => 21
[8]
 => 34
[7,1]
 => 34
[6,2]
 => 44
[6,1,1]
 => 34
[5,3]
 => 54
[5,2,1]
 => 38
Description
The number of monomer-dimer tilings of a Ferrers diagram. For a hook of length $n$, this is the $n$-th Fibonacci number.
Matching statistic: St000468
Mapping
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000468: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 4%●distinct values known / distinct values provided: 3%
Values
[1]
 => [[1],[]]
 => ([],1)
 => ([],1)
 => 1
[2]
 => [[2],[]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
[1,1]
 => [[1,1],[]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
[3]
 => [[3],[]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 3
[2,1]
 => [[2,1],[]]
 => ([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,1,1]
 => [[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 3
[4]
 => [[4],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 5
[3,1]
 => [[3,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 5
[2,2]
 => [[2,2],[]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 7
[2,1,1]
 => [[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 5
[1,1,1,1]
 => [[1,1,1,1],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 5
[5]
 => [[5],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 8
[4,1]
 => [[4,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 8
[3,2]
 => [[3,2],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 10
[3,1,1]
 => [[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 8
[2,2,1]
 => [[2,2,1],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 10
[2,1,1,1]
 => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 8
[1,1,1,1,1]
 => [[1,1,1,1,1],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 8
[6]
 => [[6],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 13
[5,1]
 => [[5,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 13
[4,2]
 => [[4,2],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 17
[4,1,1]
 => [[4,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 13
[3,3]
 => [[3,3],[]]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 22
[3,2,1]
 => [[3,2,1],[]]
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 14
[3,1,1,1]
 => [[3,1,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 13
[2,2,2]
 => [[2,2,2],[]]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 22
[2,2,1,1]
 => [[2,2,1,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 17
[2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 13
[1,1,1,1,1,1]
 => [[1,1,1,1,1,1],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 13
[7]
 => [[7],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 21
[6,1]
 => [[6,1],[]]
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 21
[5,2]
 => [[5,2],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 27
[5,1,1]
 => [[5,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 21
[4,3]
 => [[4,3],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 32
[4,2,1]
 => [[4,2,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => 24
[4,1,1,1]
 => [[4,1,1,1],[]]
 => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 21
[3,3,1]
 => [[3,3,1],[]]
 => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 32
[3,2,2]
 => [[3,2,2],[]]
 => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 32
[3,2,1,1]
 => [[3,2,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => 24
[3,1,1,1,1]
 => [[3,1,1,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 21
[2,2,2,1]
 => [[2,2,2,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 32
[2,2,1,1,1]
 => [[2,2,1,1,1],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 27
[2,1,1,1,1,1]
 => [[2,1,1,1,1,1],[]]
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 21
[1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 21
[8]
 => [[8],[]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 34
[7,1]
 => [[7,1],[]]
 => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 34
[6,2]
 => [[6,2],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
 => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,7),(4,7),(5,7)],8)
 => ? = 44
[6,1,1]
 => [[6,1,1],[]]
 => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 34
[5,3]
 => [[5,3],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => ? = 54
[5,2,1]
 => [[5,2,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
 => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8)
 => ? = 38
[5,1,1,1]
 => [[5,1,1,1],[]]
 => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 34
[4,4]
 => [[4,4],[]]
 => ([(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)
 => ? = 71
[4,3,1]
 => [[4,3,1],[]]
 => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 47
[4,2,2]
 => [[4,2,2],[]]
 => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => ? = 54
[4,2,1,1]
 => [[4,2,1,1],[]]
 => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 41
[4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 34
[3,3,2]
 => [[3,3,2],[]]
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)
 => ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 67
[3,3,1,1]
 => [[3,3,1,1],[]]
 => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => ? = 54
[3,2,2,1]
 => [[3,2,2,1],[]]
 => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 47
[3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
 => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8)
 => ? = 38
[3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 34
[2,2,2,2]
 => [[2,2,2,2],[]]
 => ([(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)
 => ? = 71
[2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => ? = 54
[2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
 => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,7),(4,7),(5,7)],8)
 => ? = 44
[2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 34
[1,1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1,1],[]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 34
[9]
 => [[9],[]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 55
[8,1]
 => [[8,1],[]]
 => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 55
[7,2]
 => [[7,2],[]]
 => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)
 => ([(0,7),(1,3),(1,4),(2,5),(2,6),(3,7),(4,8),(5,8),(6,8)],9)
 => ? = 71
[7,1,1]
 => [[7,1,1],[]]
 => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 55
[6,3]
 => [[6,3],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)
 => ([(0,5),(1,2),(1,6),(2,8),(3,5),(3,7),(4,6),(4,7),(6,8),(7,8)],9)
 => ? = 86
[6,2,1]
 => [[6,2,1],[]]
 => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)
 => ([(0,8),(1,6),(2,3),(2,6),(3,7),(4,7),(4,8),(5,7),(5,8)],9)
 => ? = 62
[6,1,1,1]
 => [[6,1,1,1],[]]
 => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 55
[5,4]
 => [[5,4],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(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)
 => ? = 103
[5,3,1]
 => [[5,3,1],[]]
 => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)
 => ([(0,8),(1,4),(2,6),(2,7),(3,5),(3,8),(4,7),(5,6),(5,7),(6,8)],9)
 => ? = 79
[5,2,2]
 => [[5,2,2],[]]
 => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)
 => ([(0,5),(1,2),(1,6),(2,8),(3,5),(3,7),(4,6),(4,7),(6,8),(7,8)],9)
 => ? = 86
[5,2,1,1]
 => [[5,2,1,1],[]]
 => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)
 => ([(0,6),(1,5),(2,5),(2,8),(3,7),(3,8),(4,7),(4,8),(6,7)],9)
 => ? = 65
[5,1,1,1,1]
 => [[5,1,1,1,1],[]]
 => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 55
[4,4,1]
 => [[4,4,1],[]]
 => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(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)
 => ? = 103
[4,3,2]
 => [[4,3,2],[]]
 => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)
 => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
 => ? = 97
[4,3,1,1]
 => [[4,3,1,1],[]]
 => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)
 => ([(0,8),(1,4),(2,6),(2,7),(3,5),(3,8),(4,7),(5,6),(5,7),(6,8)],9)
 => ? = 79
[4,2,2,1]
 => [[4,2,2,1],[]]
 => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)
 => ([(0,8),(1,4),(2,6),(2,7),(3,5),(3,8),(4,7),(5,6),(5,7),(6,8)],9)
 => ? = 79
[4,2,1,1,1]
 => [[4,2,1,1,1],[]]
 => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)
 => ([(0,6),(1,5),(2,5),(2,8),(3,7),(3,8),(4,7),(4,8),(6,7)],9)
 => ? = 65
[4,1,1,1,1,1]
 => [[4,1,1,1,1,1],[]]
 => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 55
[3,3,3]
 => [[3,3,3],[]]
 => ([(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)
 => ? = 131
[3,3,2,1]
 => [[3,3,2,1],[]]
 => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)
 => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
 => ? = 97
[3,3,1,1,1]
 => [[3,3,1,1,1],[]]
 => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)
 => ([(0,5),(1,2),(1,6),(2,8),(3,5),(3,7),(4,6),(4,7),(6,8),(7,8)],9)
 => ? = 86
[3,2,2,2]
 => [[3,2,2,2],[]]
 => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(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)
 => ? = 103
[3,2,2,1,1]
 => [[3,2,2,1,1],[]]
 => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)
 => ([(0,8),(1,4),(2,6),(2,7),(3,5),(3,8),(4,7),(5,6),(5,7),(6,8)],9)
 => ? = 79
[3,2,1,1,1,1]
 => [[3,2,1,1,1,1],[]]
 => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)
 => ([(0,8),(1,6),(2,3),(2,6),(3,7),(4,7),(4,8),(5,7),(5,8)],9)
 => ? = 62
[3,1,1,1,1,1,1]
 => [[3,1,1,1,1,1,1],[]]
 => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 55
[2,2,2,2,1]
 => [[2,2,2,2,1],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(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)
 => ? = 103
[2,2,2,1,1,1]
 => [[2,2,2,1,1,1],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)
 => ([(0,5),(1,2),(1,6),(2,8),(3,5),(3,7),(4,6),(4,7),(6,8),(7,8)],9)
 => ? = 86
[2,2,1,1,1,1,1]
 => [[2,2,1,1,1,1,1],[]]
 => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)
 => ([(0,7),(1,3),(1,4),(2,5),(2,6),(3,7),(4,8),(5,8),(6,8)],9)
 => ? = 71
Description
The Hosoya index of a graph. This is the total number of matchings in the graph.