Identifier
Values
01 => 01 => [1,1] => ([(0,1)],2) => -1
10 => 01 => [1,1] => ([(0,1)],2) => -1
001 => 001 => [2,1] => ([(0,2),(1,2)],3) => 0
010 => 001 => [2,1] => ([(0,2),(1,2)],3) => 0
011 => 011 => [1,2] => ([(1,2)],3) => 0
100 => 001 => [2,1] => ([(0,2),(1,2)],3) => 0
101 => 011 => [1,2] => ([(1,2)],3) => 0
110 => 011 => [1,2] => ([(1,2)],3) => 0
0001 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
0010 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
0011 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 0
0100 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
0101 => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => -1
0110 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 0
0111 => 0111 => [1,3] => ([(2,3)],4) => 0
1000 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
1001 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 0
1010 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 0
1011 => 0111 => [1,3] => ([(2,3)],4) => 0
1100 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 0
1101 => 0111 => [1,3] => ([(2,3)],4) => 0
1110 => 0111 => [1,3] => ([(2,3)],4) => 0
00001 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
00010 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
00011 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
00100 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
00101 => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
00110 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
00111 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 0
01000 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
01001 => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
01010 => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
01011 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
01100 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
01101 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
01110 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 0
01111 => 01111 => [1,4] => ([(3,4)],5) => 0
10000 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
10001 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
10010 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
10011 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 0
10100 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
10101 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
10110 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 0
10111 => 01111 => [1,4] => ([(3,4)],5) => 0
11000 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
11001 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 0
11010 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 0
11011 => 01111 => [1,4] => ([(3,4)],5) => 0
11100 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 0
11101 => 01111 => [1,4] => ([(3,4)],5) => 0
11110 => 01111 => [1,4] => ([(3,4)],5) => 0
000001 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
000010 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
000011 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
000100 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
000101 => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
000110 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
000111 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
001000 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
001010 => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
001011 => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
001100 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
001110 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
001111 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
010000 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
010001 => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
010010 => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
010100 => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
010101 => 010101 => [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) => -1
010110 => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
010111 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
011000 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
011001 => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
011010 => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
011100 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
011101 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
011110 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
011111 => 011111 => [1,5] => ([(4,5)],6) => 0
100000 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
100001 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
100010 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
100011 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
100100 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
100101 => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
100110 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
100111 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
101000 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
101001 => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
101010 => 001011 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
101011 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
101100 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
101101 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
101110 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
101111 => 011111 => [1,5] => ([(4,5)],6) => 0
110000 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
110001 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
110010 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
110011 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
110100 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
110101 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
>>> Load all 216 entries. <<<
110110 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
110111 => 011111 => [1,5] => ([(4,5)],6) => 0
111000 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
111001 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
111010 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
111011 => 011111 => [1,5] => ([(4,5)],6) => 0
111100 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 0
111101 => 011111 => [1,5] => ([(4,5)],6) => 0
111110 => 011111 => [1,5] => ([(4,5)],6) => 0
0000001 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0000010 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0000011 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0000100 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0000101 => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0000110 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0000111 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
0001000 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0001010 => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0001011 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0001100 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0001110 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
0001111 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
0010000 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0010100 => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0010101 => 0010101 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0010110 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0010111 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0011000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0011100 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
0011110 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
0011111 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
0100000 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0100001 => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0100010 => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0100100 => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0100101 => 0010101 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0101000 => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0101001 => 0010101 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0101010 => 0010101 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0101011 => 0101011 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0101100 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0101101 => 0101011 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0101110 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0101111 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0110000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
0110001 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0110010 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0110100 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0110101 => 0101011 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0111000 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
0111001 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0111010 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0111100 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
0111101 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
0111110 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
0111111 => 0111111 => [1,6] => ([(5,6)],7) => 0
1000000 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
1000001 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
1000010 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
1000011 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1000100 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
1000101 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1000110 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1000111 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1001000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
1001010 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1001011 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1001100 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1001110 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1001111 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1010000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
1010001 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1010010 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1010100 => 0001011 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1010101 => 0101011 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1010110 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1010111 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1011000 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1011001 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1011010 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1011100 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1011101 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1011110 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1011111 => 0111111 => [1,6] => ([(5,6)],7) => 0
1100000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
1100001 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1100010 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1100011 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1100100 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1100101 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1100110 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1100111 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1101000 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1101001 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1101010 => 0010111 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1101011 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1101100 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1101101 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1101110 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1101111 => 0111111 => [1,6] => ([(5,6)],7) => 0
1110000 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
1110001 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1110010 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1110011 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1110100 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1110101 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
1110110 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1110111 => 0111111 => [1,6] => ([(5,6)],7) => 0
1111000 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
1111001 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1111010 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1111011 => 0111111 => [1,6] => ([(5,6)],7) => 0
1111100 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 0
1111101 => 0111111 => [1,6] => ([(5,6)],7) => 0
1111110 => 0111111 => [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
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
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.