Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000510
(load all 2 compositions to match this statistic)
Mapping
St000510: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 1
[1,1]
 => 1
[3]
 => 2
[2,1]
 => 0
[1,1,1]
 => 2
[4]
 => 2
[3,1]
 => 0
[2,2]
 => 2
[2,1,1]
 => 0
[1,1,1,1]
 => 6
[5]
 => 4
[4,1]
 => 0
[3,2]
 => 0
[3,1,1]
 => 0
[2,2,1]
 => 0
[2,1,1,1]
 => 0
[1,1,1,1,1]
 => 24
[6]
 => 2
[5,1]
 => 0
[4,2]
 => 0
[4,1,1]
 => 0
[3,3]
 => 6
[3,2,1]
 => 0
[3,1,1,1]
 => 0
[2,2,2]
 => 8
[2,2,1,1]
 => 0
[2,1,1,1,1]
 => 0
[1,1,1,1,1,1]
 => 120
[7]
 => 6
[6,1]
 => 0
[5,2]
 => 0
[5,1,1]
 => 0
[4,3]
 => 0
[4,2,1]
 => 0
[4,1,1,1]
 => 0
[3,3,1]
 => 0
[3,2,2]
 => 0
[3,2,1,1]
 => 0
[3,1,1,1,1]
 => 0
[2,2,2,1]
 => 0
[2,2,1,1,1]
 => 0
[2,1,1,1,1,1]
 => 0
[1,1,1,1,1,1,1]
 => 720
[8]
 => 4
[7,1]
 => 0
[6,2]
 => 0
[6,1,1]
 => 0
[5,3]
 => 0
[5,2,1]
 => 0
[5,1,1,1]
 => 0
Description
The number of invariant oriented cycles when acting with a permutation of given cycle type.
Matching statistic: St000264
(load all 6 compositions to match this statistic)
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 59%●distinct values known / distinct values provided: 4%
Values
[2]
 => [1,1,0,0,1,0]
 => [2,1] => ([(0,2),(1,2)],3)
 => ? = 1 + 3
[1,1]
 => [1,0,1,1,0,0]
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 3
[3]
 => [1,1,1,0,0,0,1,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 2 + 3
[2,1]
 => [1,0,1,0,1,0]
 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 0 + 3
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,3] => ([(2,3)],4)
 => ? = 2 + 3
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 2 + 3
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 0 + 3
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 3
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 0 + 3
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,4] => ([(3,4)],5)
 => ? = 6 + 3
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 4 + 3
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 0 + 3
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 0 + 3
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3 = 0 + 3
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,5] => ([(4,5)],6)
 => ? = 24 + 3
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 + 3
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 6 + 3
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 0 + 3
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 8 + 3
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,6] => ([(5,6)],7)
 => ? = 120 + 3
[7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 6 + 3
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,7] => ([(6,7)],8)
 => ? = 720 + 3
[8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [8,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ? = 4 + 3
[7,1]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[5,1,1,1]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 8 + 3
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[4,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[3,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? = 48 + 3
[2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[1,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [1,8] => ([(7,8)],9)
 => ? = 5040 + 3
[9]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
 => [9,1] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
 => ? = 6 + 3
[8,1]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
 => [7,1,1] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 0 + 3
[7,2]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
 => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[7,1,1]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
 => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[6,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(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)
 => 3 = 0 + 3
[6,1,1,1]
 => [1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 36 + 3
[3,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [1,5,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,7,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 0 + 3
[1,1,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
 => [1,9] => ([(8,9)],10)
 => ? = 40320 + 3
[10]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
 => [10,1] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
 => ? = 4 + 3
[9,1]
 => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
 => [8,1,1] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 0 + 3
[8,2]
 => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
 => [7,1,1] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 0 + 3
[8,1,1]
 => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
 => [6,2,1] => ([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 0 + 3
[7,3]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
 => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[7,2,1]
 => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
 => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[7,1,1,1]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
 => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 20 + 3
[4,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[3,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[3,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
 => [1,7,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 0 + 3
[2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [2,5] => ([(4,6),(5,6)],7)
 => ? = 384 + 3
[2,2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 3
[2,2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
 => [1,6,2] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 0 + 3
[2,1,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1,8,1] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 0 + 3
[1,1,1,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
 => [1,10] => ([(9,10)],11)
 => ? = 362880 + 3
[11]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [11,1] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
 => ? = 10 + 3
[10,1]
 => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
 => [9,1,1] => ?
 => ? = 0 + 3
[9,2]
 => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
 => [8,1,1] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 0 + 3
[9,1,1]
 => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
 => [7,2,1] => ([(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 0 + 3
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.