Identifier
Values
[1,0,1,0] => [2,1] => [1,1] => ([(0,1)],2) => -1
[1,0,1,0,1,0] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3) => 0
[1,0,1,1,0,0] => [2,1,3] => [1,2] => ([(1,2)],3) => 0
[1,1,0,0,1,0] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3) => 0
[1,1,0,1,0,0] => [3,1,2] => [1,2] => ([(1,2)],3) => 0
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4) => 0
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4) => 0
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [1,3] => ([(2,3)],4) => 0
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4) => 0
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4) => 0
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [1,3] => ([(2,3)],4) => 0
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4) => 0
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [1,3] => ([(2,3)],4) => 0
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [1,4] => ([(3,4)],5) => 0
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [1,4] => ([(3,4)],5) => 0
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [1,4] => ([(3,4)],5) => 0
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 0
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [1,4] => ([(3,4)],5) => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,5] => ([(4,5)],6) => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [1,5] => ([(4,5)],6) => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [1,5] => ([(4,5)],6) => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [1,5] => ([(4,5)],6) => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [1,5] => ([(4,5)],6) => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
>>> Load all 219 entries. <<<
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [1,6] => ([(5,6)],7) => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [1,6] => ([(5,6)],7) => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [1,6] => ([(5,6)],7) => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [1,6] => ([(5,6)],7) => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [1,6] => ([(5,6)],7) => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [2,5] => ([(4,6),(5,6)],7) => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [1,6] => ([(5,6)],7) => 0
search for individual values
searching the database for the individual values of this statistic
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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.