Identifier
Values
[3,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[3,2,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[5,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[3,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[3,2,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,2,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[4,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[3,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[3,2,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[3,2,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[7,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[5,4,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[5,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,2,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,3,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[3,3,2,1,1] => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[3,2,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[3,2,2,1,1,1] => 100111 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,1,1,1,1,1] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[7,2,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[6,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[5,4,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[5,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,2,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,2,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,3,2,2] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[4,3,2,1,1] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[3,3,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[3,3,2,1,1,1] => 110111 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,2,2,1,1] => 100011 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,2,1,1,1,1] => 1001111 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[9,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,4,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,2,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[6,3,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,4,3] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[5,4,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,4,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,3,2,1,1] => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,2,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,2,2,1,1,1] => 100111 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,1,1,1,1,1] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[4,3,3,2] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[4,3,2,2,1] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,2,1,1,1] => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,3,3,2,1] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[3,3,2,2,1,1] => 110011 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,3,2,1,1,1,1] => 1101111 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,2,2,2,2,1] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,2,2,1,1,1] => 1000111 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[9,2,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[8,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,4,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,2,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,2,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,5,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[6,3,2,2] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[6,3,2,1,1] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,5,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,4,3,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[5,4,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,3,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,3,2,1,1,1] => 110111 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,2,2,1,1] => 100011 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,2,1,1,1,1] => 1001111 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,4,3,2] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[4,3,3,2,1] => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,2,2,2] => 01000 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,3,2,2,1,1] => 010011 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,1,1,1,1] => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,3,3,2,1,1] => 111011 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,3,2,2,2,1] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,3,2,2,1,1,1] => 1100111 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,2,2,2,2,1,1] => 1000011 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[11,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[9,4,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[9,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,2,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[8,3,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,6,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,4,3] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,4,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,4,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[7,3,2,1,1] => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,2,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,2,2,1,1,1] => 100111 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,2,1,1,1,1,1] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[6,5,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,3,3,2] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,3,2,2,1] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,3,2,1,1,1] => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,5,2,1,1] => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,4,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,4,3,2] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,4,3,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,4,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,2,1,1,1] => 100111 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,1,1,1,1,1] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
>>> Load all 315 entries. <<<
[5,3,3,2,1] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,3,2,2,1,1] => 110011 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,1,1,1,1] => 1101111 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,2,2,2,1] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,2,2,1,1,1] => 1000111 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,4,3,2,1] => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,3,2,2] => 01100 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,3,2,1,1] => 011011 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,2,2,1] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,2,1,1,1] => 0100111 => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,3,3,2,2,1] => 111001 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,3,3,2,1,1,1] => 1110111 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,3,2,2,2,1,1] => 1100011 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,2,2,2,2,2,1] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[11,2,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[10,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[9,4,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[9,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,2,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[9,2,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[8,5,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[8,3,2,2] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[8,3,2,1,1] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,6,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,5,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,4,3,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,4,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,4,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[7,3,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,3,2,1,1,1] => 110111 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,2,2,2,1,1] => 100011 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,2,2,1,1,1,1] => 1001111 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,5,4] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[6,5,2,2] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[6,5,2,1,1] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,4,3,2] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,3,3,2,1] => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,3,2,2,2] => 01000 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[6,3,2,2,1,1] => 010011 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,2,1,1,1,1] => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,5,4,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,5,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,5,2,1,1,1] => 110111 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,4,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,3,3] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[5,4,3,2,1] => 10101 => [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
[5,4,3,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,4,2,2,1,1] => 100011 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,2,1,1,1,1] => 1001111 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,3,2,1,1] => 111011 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,2,2,1] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,2,1,1,1] => 1100111 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,2,2,2,1,1] => 1000011 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,4,3,2,2] => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,4,3,2,1,1] => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,3,3,2] => 01110 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,3,2,2,1] => 011001 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,3,2,1,1,1] => 0110111 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,2,2,2] => 010000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,3,2,2,2,1,1] => 0100011 => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,3,3,3,2,1] => 111101 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,3,3,2,2,1,1] => 1110011 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,3,2,2,2,2,1] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[13,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[11,4,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[11,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[11,2,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[10,3,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,6,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[9,4,3] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[9,4,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,4,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[9,3,2,1,1] => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[9,2,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[9,2,2,1,1,1] => 100111 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[9,2,1,1,1,1,1] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[8,5,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[8,3,3,2] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[8,3,2,2,1] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,3,2,1,1,1] => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,6,3] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,6,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,6,1,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[7,5,2,1,1] => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,4,4,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,4,3,2] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,4,3,1,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[7,4,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,4,2,1,1,1] => 100111 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,4,1,1,1,1,1] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[7,3,3,2,1] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,3,2,2,1,1] => 110011 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,3,2,1,1,1,1] => 1101111 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,2,2,2,1] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,2,2,2,1,1,1] => 1000111 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,5,4,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,5,3,2] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,5,2,2,1] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,5,2,1,1,1] => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,4,3,2,1] => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,3,3,2,2] => 01100 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,3,3,2,1,1] => 011011 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,2,2,2,1] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,2,2,1,1,1] => 0100111 => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,5,4,1,1] => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,5,3,2,1] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,5,2,2,1,1] => 110011 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,5,2,1,1,1,1] => 1101111 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,4,4,3] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,4,4,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,4,1,1,1] => 100111 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,3,3,1] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,4,3,2,2] => 10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,3,2,1,1] => 101011 => [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
[5,4,3,1,1,1,1] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[5,4,2,2,2,1] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,2,2,1,1,1] => 1000111 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,3,2,2,1] => 111001 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,3,2,1,1,1] => 1110111 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,2,2,1,1] => 1100011 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,2,2,2,2,1] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,4,3,3,2] => 00110 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,4,3,2,2,1] => 001001 => [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) => 3
[4,4,3,2,1,1,1] => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,3,3,2,1] => 011101 => [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
[4,3,3,2,2,2] => 011000 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,3,2,2,1,1] => 0110011 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,2,2,2,1] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,3,3,3,2,1,1] => 1111011 => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,3,3,2,2,2,1] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[13,2,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[12,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[11,4,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[11,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[11,2,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[11,2,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[10,5,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[10,3,2,2] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[10,3,2,1,1] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[9,6,1,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[9,5,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,4,3,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[9,4,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[9,4,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[9,3,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[9,3,2,1,1,1] => 110111 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[9,2,2,2,1,1] => 100011 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[9,2,2,1,1,1,1] => 1001111 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[8,7,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[8,5,4] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[8,5,2,2] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[8,5,2,1,1] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,4,3,2] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[8,3,3,2,1] => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,3,2,2,2] => 01000 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[8,3,2,2,1,1] => 010011 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[8,3,2,1,1,1,1] => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,7,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,6,3,1] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,6,2,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,6,1,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[7,5,4,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,5,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,5,2,1,1,1] => 110111 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,4,4,1,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,4,3,3] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,4,3,2,1] => 10101 => [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
[7,4,3,1,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[7,4,2,2,1,1] => 100011 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,4,2,1,1,1,1] => 1001111 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,3,2,1,1] => 111011 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,3,2,2,2,1] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,3,2,2,1,1,1] => 1100111 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,2,2,2,1,1] => 1000011 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,6,3,2] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,5,4,2] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[6,5,4,1,1] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,5,3,2,1] => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,5,2,2,2] => 01000 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[6,5,2,2,1,1] => 010011 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,5,2,1,1,1,1] => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,4,3,2,2] => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,4,3,2,1,1] => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,3,3,2] => 01110 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,3,3,2,2,1] => 011001 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,3,2,1,1,1] => 0110111 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,2,2,2] => 010000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,3,2,2,2,1,1] => 0100011 => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,5,4,3] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,5,4,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,5,4,1,1,1] => 110111 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,5,3,2,1,1] => 111011 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,5,2,2,2,1] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,5,2,2,1,1,1] => 1100111 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,4,4,3,1] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,4,2,1,1] => 100011 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,4,1,1,1,1] => 1001111 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,4,3,3,2] => 10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,3,3,1,1] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,4,3,2,2,1] => 101001 => [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) => 3
[5,4,3,2,1,1,1] => 1010111 => [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) => 3
[5,4,2,2,2,1,1] => 1000011 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,3,3,2,1] => 111101 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,3,2,2,1,1] => 1110011 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,2,2,2,1] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,4,4,3,2] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,4,3,3,2,1] => 001101 => [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) => 3
[4,4,3,2,2,2] => 001000 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,4,3,2,2,1,1] => 0010011 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,3,3,2,2] => 011100 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,3,3,2,1,1] => 0111011 => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,3,2,2,2,1] => 0110001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,2,2,2,2] => 0100000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[3,3,3,3,2,2,1] => 1111001 => [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
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
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
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
odd parts
Description
Return the binary word indicating which parts of the partition are odd.