Identifier
Values
[1,0] => [1] => [1] => ([],1) => 0
[1,0,1,0] => [1,1] => [2] => ([],2) => 0
[1,1,0,0] => [2] => [1,1] => ([(0,1)],2) => 1
[1,0,1,0,1,0] => [1,1,1] => [3] => ([],3) => 0
[1,1,0,0,1,0] => [2,1] => [1,2] => ([(1,2)],3) => 1
[1,1,0,1,0,0] => [2,1] => [1,2] => ([(1,2)],3) => 1
[1,1,1,0,0,0] => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [4] => ([],4) => 0
[1,1,0,0,1,0,1,0] => [2,1,1] => [1,3] => ([(2,3)],4) => 1
[1,1,0,1,0,0,1,0] => [2,1,1] => [1,3] => ([(2,3)],4) => 1
[1,1,0,1,0,1,0,0] => [2,1,1] => [1,3] => ([(2,3)],4) => 1
[1,1,1,0,0,0,1,0] => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0] => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,0,0] => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,0,0] => [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [5] => ([],5) => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,4] => ([(3,4)],5) => 1
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => [1,4] => ([(3,4)],5) => 1
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => [1,4] => ([(3,4)],5) => 1
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => [1,4] => ([(3,4)],5) => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,1,0,0,0,1,0,0] => [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,1,0,0,1,0,0,0] => [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,1,0,1,0,0,0,0] => [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,1,1,0,0,0,0,0] => [5] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [6] => ([],6) => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,5] => ([(4,5)],6) => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,5] => ([(4,5)],6) => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => [1,5] => ([(4,5)],6) => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => [1,5] => ([(4,5)],6) => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => [1,5] => ([(4,5)],6) => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [7] => ([],7) => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,6] => ([(5,6)],7) => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,6] => ([(5,6)],7) => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,6] => ([(5,6)],7) => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => [1,6] => ([(5,6)],7) => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => [1,6] => ([(5,6)],7) => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => [1,6] => ([(5,6)],7) => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
>>> Load all 143 entries. <<<
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [1,1,1,1,1,2] => ([(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) => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1] => [1,1,1,1,1,2] => ([(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) => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => [1,1,1,1,1,2] => ([(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) => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => [1,1,1,1,1,2] => ([(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) => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => [1,1,1,1,1,2] => ([(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) => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => [1,1,1,1,1,2] => ([(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) => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => ([(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) => 6
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.