Identifier
Values
[1,2,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[2,1,3] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[1,2,3,4] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,2,4,3] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,3,2,4] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[2,1,3,4] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[2,1,4,3] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[2,3,1,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[3,1,2,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[3,2,1,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,2,3,4,5] => 1111 => [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) => 3
[1,2,3,5,4] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,2,4,3,5] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,3,2,4,5] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,3,2,5,4] => 1010 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,3,4,2,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,2,3,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,3,2,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,1,3,4,5] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,1,3,5,4] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,1,4,3,5] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,3,1,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,3,1,5,4] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,3,4,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,4,1,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,4,3,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[3,1,2,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,1,2,5,4] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,1,4,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[3,2,1,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,2,1,5,4] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,2,4,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[3,4,1,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[3,4,2,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[4,1,2,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[4,1,3,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[4,2,1,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[4,2,3,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[4,3,1,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[4,3,2,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,2,3,4,5,6] => 11111 => [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) => 2
[1,2,3,4,6,5] => 11110 => [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) => 3
[1,2,3,5,4,6] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,4,3,5,6] => 11011 => [1,1,2,1,1] => ([(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) => 2
[1,2,4,3,6,5] => 11010 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,4,5,3,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,3,4,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,4,3,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,4,6,5] => 10110 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,5,4,6] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,4,2,5,6] => 10011 => [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) => 2
[1,3,4,2,6,5] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,4,5,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,5,2,4,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,5,4,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,2,3,5,6] => 10011 => [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) => 2
[1,4,2,3,6,5] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,2,5,3,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,3,2,5,6] => 10011 => [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) => 2
[1,4,3,2,6,5] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,3,5,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,5,2,3,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,5,3,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,2,3,4,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,2,4,3,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,3,2,4,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,3,4,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,2,3,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,3,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,1,3,4,5,6] => 01111 => [2,1,1,1,1] => ([(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) => 2
[2,1,3,4,6,5] => 01110 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,3,5,4,6] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,3,5,6] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,3,6,5] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,5,3,6] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,3,4,6] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,4,3,6] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,1,4,6,5] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,1,5,4,6] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,4,1,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,3,4,1,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,4,5,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,3,5,1,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,3,5,4,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,4,1,3,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,4,1,3,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,1,5,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,4,3,1,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,4,3,1,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,3,5,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,4,5,1,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,4,5,3,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,5,1,3,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,5,1,4,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,5,3,1,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,5,3,4,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,5,4,1,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,5,4,3,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,1,2,4,6,5] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,2,5,4,6] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,4,2,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
>>> Load all 180 entries. <<<
[3,1,4,2,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,4,5,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,1,5,2,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,1,5,4,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,2,1,4,6,5] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,1,5,4,6] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,4,1,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,4,1,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,4,5,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,2,5,1,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,2,5,4,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,4,1,2,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,4,1,2,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,1,5,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,4,2,1,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,4,2,1,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,2,5,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,4,5,1,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,4,5,2,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,5,1,2,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,5,1,4,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,5,2,1,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,5,2,4,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,5,4,1,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,5,4,2,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,1,2,3,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,2,3,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,2,5,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,1,3,2,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,3,2,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,3,5,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,1,5,2,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,1,5,3,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,2,1,3,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,1,3,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,1,5,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,2,3,1,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,3,1,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,3,5,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,2,5,1,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,2,5,3,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,3,1,2,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,1,2,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,1,5,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,3,2,1,5,6] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,1,6,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,2,5,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,3,5,1,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,3,5,2,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,5,1,2,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,5,1,3,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,5,2,1,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,5,2,3,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,5,3,1,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,5,3,2,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,1,2,3,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,1,2,4,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,1,3,2,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,1,3,4,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,1,4,2,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,1,4,3,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,2,1,3,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,2,1,4,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,2,3,1,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,2,3,4,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,2,4,1,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,2,4,3,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,3,1,2,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,3,1,4,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,3,2,1,4,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,3,2,4,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,3,4,1,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,3,4,2,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,4,1,2,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,4,1,3,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,4,2,1,3,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,4,2,3,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,4,3,1,2,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[5,4,3,2,1,6] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
search for individual values
searching the database for the individual values of this statistic
Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
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
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.