Identifier
Values
0 => 0 => [1] => ([],1) => 1
1 => 1 => [1] => ([],1) => 1
00 => 00 => [2] => ([],2) => 2
01 => 01 => [1,1] => ([(0,1)],2) => 1
10 => 01 => [1,1] => ([(0,1)],2) => 1
11 => 11 => [2] => ([],2) => 2
000 => 000 => [3] => ([],3) => 3
001 => 001 => [2,1] => ([(0,2),(1,2)],3) => 1
010 => 001 => [2,1] => ([(0,2),(1,2)],3) => 1
011 => 011 => [1,2] => ([(1,2)],3) => 2
100 => 001 => [2,1] => ([(0,2),(1,2)],3) => 1
101 => 011 => [1,2] => ([(1,2)],3) => 2
110 => 011 => [1,2] => ([(1,2)],3) => 2
111 => 111 => [3] => ([],3) => 3
0000 => 0000 => [4] => ([],4) => 4
0001 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
0010 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
0011 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 2
0100 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
0101 => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0110 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 2
0111 => 0111 => [1,3] => ([(2,3)],4) => 3
1000 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
1001 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 2
1010 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 2
1011 => 0111 => [1,3] => ([(2,3)],4) => 3
1100 => 0011 => [2,2] => ([(1,3),(2,3)],4) => 2
1101 => 0111 => [1,3] => ([(2,3)],4) => 3
1110 => 0111 => [1,3] => ([(2,3)],4) => 3
1111 => 1111 => [4] => ([],4) => 4
00000 => 00000 => [5] => ([],5) => 5
00001 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
00010 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
00011 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
00100 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
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) => 3
00110 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
00111 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 3
01000 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
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) => 3
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) => 3
01011 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
01100 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
01101 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
01110 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 3
01111 => 01111 => [1,4] => ([(3,4)],5) => 4
10000 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
10001 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
10010 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
10011 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 3
10100 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
10101 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
10110 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 3
10111 => 01111 => [1,4] => ([(3,4)],5) => 4
11000 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
11001 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 3
11010 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 3
11011 => 01111 => [1,4] => ([(3,4)],5) => 4
11100 => 00111 => [2,3] => ([(2,4),(3,4)],5) => 3
11101 => 01111 => [1,4] => ([(3,4)],5) => 4
11110 => 01111 => [1,4] => ([(3,4)],5) => 4
11111 => 11111 => [5] => ([],5) => 5
000000 => 000000 => [6] => ([],6) => 6
000001 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
000010 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
000011 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
000100 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
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) => 3
000110 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
000111 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
001000 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
001001 => 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
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) => 3
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) => 3
001100 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
001101 => 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
001110 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
001111 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
010000 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
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) => 3
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) => 3
010011 => 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
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) => 3
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) => 5
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) => 3
010111 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
011000 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
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) => 3
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) => 3
011011 => 011011 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011100 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
011101 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
011110 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
011111 => 011111 => [1,5] => ([(4,5)],6) => 5
100000 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
100001 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
100010 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
100011 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
100100 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
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) => 3
100110 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
>>> Load all 254 entries. <<<
100111 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
101000 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
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) => 3
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) => 3
101011 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
101100 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
101101 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
101110 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
101111 => 011111 => [1,5] => ([(4,5)],6) => 5
110000 => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 3
110001 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
110010 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
110011 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
110100 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
110101 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
110110 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
110111 => 011111 => [1,5] => ([(4,5)],6) => 5
111000 => 000111 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
111001 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
111010 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
111011 => 011111 => [1,5] => ([(4,5)],6) => 5
111100 => 001111 => [2,4] => ([(3,5),(4,5)],6) => 4
111101 => 011111 => [1,5] => ([(4,5)],6) => 5
111110 => 011111 => [1,5] => ([(4,5)],6) => 5
111111 => 111111 => [6] => ([],6) => 6
0000000 => 0000000 => [7] => ([],7) => 7
0000001 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
0000010 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
0000011 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
0000100 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
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) => 3
0000110 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
0000111 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
0001000 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
0001001 => 0001001 => [3,1,2,1] => ([(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) => 2
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) => 3
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) => 3
0001100 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
0001101 => 0001101 => [3,2,1,1] => ([(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) => 2
0001110 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
0001111 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
0010000 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
0010001 => 0001001 => [3,1,2,1] => ([(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) => 2
0010010 => 0001001 => [3,1,2,1] => ([(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) => 2
0010011 => 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) => 2
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) => 3
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) => 5
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) => 3
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) => 3
0011000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
0011001 => 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) => 2
0011010 => 0001101 => [3,2,1,1] => ([(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) => 2
0011011 => 0011011 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0011100 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
0011101 => 0011101 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0011110 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
0011111 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
0100000 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
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) => 3
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) => 3
0100011 => 0001101 => [3,2,1,1] => ([(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) => 2
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) => 3
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) => 5
0100110 => 0001101 => [3,2,1,1] => ([(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) => 2
0100111 => 0011101 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
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) => 3
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) => 5
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) => 5
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) => 5
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) => 3
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) => 5
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) => 3
0101111 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
0110000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
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) => 3
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) => 3
0110011 => 0011011 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
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) => 3
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) => 5
0110110 => 0011011 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0110111 => 0110111 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
0111000 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
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) => 3
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) => 3
0111011 => 0110111 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
0111100 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
0111101 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
0111110 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
0111111 => 0111111 => [1,6] => ([(5,6)],7) => 6
1000000 => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
1000001 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
1000010 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
1000011 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
1000100 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
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) => 3
1000110 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
1000111 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1001000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
1001001 => 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) => 2
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) => 3
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) => 3
1001100 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
1001101 => 0011011 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1001110 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1001111 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1010000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
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) => 3
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) => 3
1010011 => 0011011 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
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) => 3
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) => 5
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) => 3
1010111 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
1011000 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
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) => 3
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) => 3
1011011 => 0110111 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
1011100 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1011101 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
1011110 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1011111 => 0111111 => [1,6] => ([(5,6)],7) => 6
1100000 => 0000011 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 4
1100001 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
1100010 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
1100011 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1100100 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
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) => 3
1100110 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1100111 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1101000 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
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) => 3
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) => 3
1101011 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
1101100 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1101101 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
1101110 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1101111 => 0111111 => [1,6] => ([(5,6)],7) => 6
1110000 => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
1110001 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1110010 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1110011 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1110100 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1110101 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
1110110 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1110111 => 0111111 => [1,6] => ([(5,6)],7) => 6
1111000 => 0001111 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 4
1111001 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1111010 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1111011 => 0111111 => [1,6] => ([(5,6)],7) => 6
1111100 => 0011111 => [2,5] => ([(4,6),(5,6)],7) => 5
1111101 => 0111111 => [1,6] => ([(5,6)],7) => 6
1111110 => 0111111 => [1,6] => ([(5,6)],7) => 6
1111111 => 1111111 => [7] => ([],7) => 7
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
click to show known generating functions       
Description
The maximal multiplicity of a Laplacian eigenvalue in a 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
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.