Identifier
Values
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,3,7,4,6,5] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,2,3,7,4,6,5] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,2,4,6,7,3,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [1,2,5,7,3,4,6] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [1,2,7,3,4,6,5] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,2,5,7,3,4,6] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [1,2,7,3,4,6,5] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,2,6,7,3,5,4] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [1,2,7,3,5,4,6] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [1,2,7,3,5,6,4] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [1,2,3,7,4,6,5] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [1,2,3,7,4,6,5] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [1,2,4,6,7,3,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [1,2,5,7,3,4,6] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [1,2,7,3,4,6,5] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [1,2,5,7,3,4,6] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [1,2,7,3,4,6,5] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [1,2,6,3,5,4,7] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [1,2,6,7,3,5,4] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [1,2,7,3,5,4,6] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [1,2,7,3,5,6,4] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [1,3,4,6,7,2,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [1,3,5,6,2,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [1,3,5,6,7,2,4] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [1,3,5,7,2,4,6] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [1,3,6,7,2,4,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [1,3,6,7,2,4,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [1,3,7,2,4,6,5] => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [1,4,5,6,2,3,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [1,4,5,7,2,3,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [1,4,6,2,3,5,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [1,4,6,7,2,3,5] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [1,7,2,3,4,6,5] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
>>> Load all 166 entries. <<<
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [1,7,2,3,4,6,5] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [1,6,2,3,5,4,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [1,6,7,2,3,5,4] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [1,7,2,3,5,4,6] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [1,7,2,3,5,6,4] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [1,7,2,3,6,4,5] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [1,7,2,3,6,4,5] => ([(1,6),(2,6),(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] => [4,3,2,5,1,6,7] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [1,4,5,6,2,3,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [1,4,5,7,2,3,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [1,4,6,2,3,5,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [1,4,6,7,2,3,5] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [1,7,2,3,4,6,5] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [1,7,2,3,4,6,5] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [1,6,2,3,5,4,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [1,6,7,2,3,5,4] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [1,7,2,3,5,4,6] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [1,7,2,3,5,6,4] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [1,7,2,3,6,4,5] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [1,7,2,3,6,4,5] => ([(1,6),(2,6),(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] => [5,4,3,2,1,6,7] => [1,5,2,4,3,6,7] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [1,5,2,4,3,6,7] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [1,5,6,2,4,3,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [1,5,6,7,2,4,3] => ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [1,5,7,2,4,3,6] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [1,6,2,4,3,5,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,6,7,2,4,3,5] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [1,7,2,4,3,5,6] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [1,7,2,4,3,5,6] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [1,6,2,4,5,3,7] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,6,7,2,4,5,3] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [1,7,2,4,5,3,6] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [1,7,2,4,5,6,3] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [1,7,2,4,6,3,5] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [1,6,2,5,3,4,7] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [1,6,7,2,5,3,4] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [1,7,2,5,3,4,6] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [1,7,2,5,6,3,4] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [1,7,2,6,3,4,5] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [1,7,2,6,3,4,5] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [1,6,2,5,3,4,7] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [1,6,7,2,5,3,4] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [1,7,2,5,3,4,6] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [1,7,2,5,6,3,4] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [1,7,2,6,3,4,5] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [1,7,2,6,3,4,5] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,7,2,6,3,5,4] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
search for individual values
searching the database for the individual values of this statistic
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.