Processing math: 100%

Identifier
Values
[1] => 1 => [1] => ([],1) => 0
[2] => 0 => [1] => ([],1) => 0
[3] => 1 => [1] => ([],1) => 0
[2,1] => 01 => [1,1] => ([(0,1)],2) => 1
[4] => 0 => [1] => ([],1) => 0
[5] => 1 => [1] => ([],1) => 0
[4,1] => 01 => [1,1] => ([(0,1)],2) => 1
[3,2] => 10 => [1,1] => ([(0,1)],2) => 1
[2,2,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[6] => 0 => [1] => ([],1) => 0
[3,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[7] => 1 => [1] => ([],1) => 0
[6,1] => 01 => [1,1] => ([(0,1)],2) => 1
[5,2] => 10 => [1,1] => ([(0,1)],2) => 1
[4,3] => 01 => [1,1] => ([(0,1)],2) => 1
[4,2,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[2,2,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8] => 0 => [1] => ([],1) => 0
[5,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[3,3,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[3,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[9] => 1 => [1] => ([],1) => 0
[8,1] => 01 => [1,1] => ([(0,1)],2) => 1
[7,2] => 10 => [1,1] => ([(0,1)],2) => 1
[6,3] => 01 => [1,1] => ([(0,1)],2) => 1
[6,2,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[5,4] => 10 => [1,1] => ([(0,1)],2) => 1
[4,4,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[4,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[4,2,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[2,2,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[10] => 0 => [1] => ([],1) => 0
[7,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[5,4,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[5,3,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[5,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[4,3,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[3,2,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[11] => 1 => [1] => ([],1) => 0
[10,1] => 01 => [1,1] => ([(0,1)],2) => 1
[9,2] => 10 => [1,1] => ([(0,1)],2) => 1
[8,3] => 01 => [1,1] => ([(0,1)],2) => 1
[8,2,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[7,4] => 10 => [1,1] => ([(0,1)],2) => 1
[6,5] => 01 => [1,1] => ([(0,1)],2) => 1
[6,4,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[6,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[6,2,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[5,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[4,4,3] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[4,4,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,2,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[3,3,3,2] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,3,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,2,2,2,2,1] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[12] => 0 => [1] => ([],1) => 0
[9,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[7,4,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[7,3,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[7,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[6,3,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[5,5,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[5,4,3] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[5,4,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[5,2,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,3,3,2] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[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) => 2
[3,3,3,2,1] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,2,2,2,2,1] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[13] => 1 => [1] => ([],1) => 0
[12,1] => 01 => [1,1] => ([(0,1)],2) => 1
[11,2] => 10 => [1,1] => ([(0,1)],2) => 1
[10,3] => 01 => [1,1] => ([(0,1)],2) => 1
[10,2,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[9,4] => 10 => [1,1] => ([(0,1)],2) => 1
[8,5] => 01 => [1,1] => ([(0,1)],2) => 1
[8,4,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[8,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[8,2,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[7,6] => 10 => [1,1] => ([(0,1)],2) => 1
[7,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[6,6,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[6,5,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[6,4,3] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[6,4,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,2,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[5,5,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[5,3,3,2] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[5,3,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,4,4,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,4,3,2] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[4,4,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[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) => 2
[4,2,2,2,2,1] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[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) => 2
[2,2,2,2,2,2,1] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[14] => 0 => [1] => ([],1) => 0
[11,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[9,4,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[9,3,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
>>> Load all 269 entries. <<<
[9,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[8,3,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[7,6,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[7,5,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[7,4,3] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[7,4,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[7,2,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[6,5,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[6,3,3,2] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[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) => 2
[5,5,4] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[5,4,4,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[5,4,3,2] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[5,4,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,3,3,2,1] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,2,2,2,2,1] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[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) => 2
[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) => 2
[3,3,3,3,2] => 11110 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[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) => 2
[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) => 2
[15] => 1 => [1] => ([],1) => 0
[14,1] => 01 => [1,1] => ([(0,1)],2) => 1
[13,2] => 10 => [1,1] => ([(0,1)],2) => 1
[12,3] => 01 => [1,1] => ([(0,1)],2) => 1
[12,2,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[11,4] => 10 => [1,1] => ([(0,1)],2) => 1
[10,5] => 01 => [1,1] => ([(0,1)],2) => 1
[10,4,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[10,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[10,2,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[9,6] => 10 => [1,1] => ([(0,1)],2) => 1
[9,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[8,7] => 01 => [1,1] => ([(0,1)],2) => 1
[8,6,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[8,5,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[8,4,3] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[8,4,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,2,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[7,5,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[7,3,3,2] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[7,3,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[6,6,3] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[6,6,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,5,4] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[6,4,4,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,4,3,2] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[6,4,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[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) => 2
[6,2,2,2,2,1] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,5,4,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[5,5,3,2] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[5,5,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[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) => 1
[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) => 2
[4,4,4,3] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,4,4,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,4,2,2,2,1] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,3,3,3,2] => 01110 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[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) => 2
[4,2,2,2,2,2,1] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[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) => 2
[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) => 2
[16] => 0 => [1] => ([],1) => 0
[13,2,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[11,4,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[11,3,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[11,2,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[10,3,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[9,6,1] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[9,5,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[9,4,3] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[9,4,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[9,2,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[8,5,2,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[8,3,3,2] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[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) => 2
[7,7,2] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[7,6,3] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[7,6,2,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[7,5,4] => 110 => [2,1] => ([(0,2),(1,2)],3) => 2
[7,4,4,1] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[7,4,3,2] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[7,4,2,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[7,3,3,2,1] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[7,2,2,2,2,1] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,4,1] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[6,5,3,2] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[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) => 2
[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) => 2
[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) => 2
[5,5,3,2,1] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,4,4,3] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[5,4,4,2,1] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,4,2,2,2,1] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,3,3,2] => 11110 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[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) => 2
[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) => 2
[4,4,3,3,2] => 00110 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[17] => 1 => [1] => ([],1) => 0
[16,1] => 01 => [1,1] => ([(0,1)],2) => 1
[15,2] => 10 => [1,1] => ([(0,1)],2) => 1
[14,3] => 01 => [1,1] => ([(0,1)],2) => 1
[14,2,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[13,4] => 10 => [1,1] => ([(0,1)],2) => 1
[12,5] => 01 => [1,1] => ([(0,1)],2) => 1
[12,4,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[12,3,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[12,2,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[11,6] => 10 => [1,1] => ([(0,1)],2) => 1
[11,3,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[10,7] => 01 => [1,1] => ([(0,1)],2) => 1
[10,6,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[10,5,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[10,4,3] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[10,4,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[10,2,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[9,8] => 10 => [1,1] => ([(0,1)],2) => 1
[9,5,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[9,3,3,2] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[9,3,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[8,8,1] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[8,7,2] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[8,6,3] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[8,6,2,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,5,4] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[8,4,4,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,4,3,2] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[8,4,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[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) => 2
[8,2,2,2,2,1] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[7,7,2,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[7,5,4,1] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[7,5,3,2] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[7,5,2,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[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) => 1
[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) => 2
[6,6,5] => 001 => [2,1] => ([(0,2),(1,2)],3) => 2
[6,6,4,1] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,6,3,2] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[6,6,2,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[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) => 2
[6,4,4,3] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,4,4,2,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[6,4,2,2,2,1] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,3,3,2] => 01110 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[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) => 2
[6,2,2,2,2,2,1] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,5,5,2] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[5,5,4,3] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[5,5,4,2,1] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[4,4,4,4,1] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,4,4,3,2] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,4,4,2,2,1] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[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) => 2
[4,4,2,2,2,2,1] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[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) => 2
[3,3,3,3,3,2] => 111110 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[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) => 2
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 diameter of a connected graph.
This is the greatest distance between any pair of vertices.
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.
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.