Identifier
Values
0 => [2] => [1,1,0,0] => 3
1 => [1,1] => [1,0,1,0] => 2
00 => [3] => [1,1,1,0,0,0] => 4
01 => [2,1] => [1,1,0,0,1,0] => 3
10 => [1,2] => [1,0,1,1,0,0] => 2
11 => [1,1,1] => [1,0,1,0,1,0] => 2
000 => [4] => [1,1,1,1,0,0,0,0] => 5
001 => [3,1] => [1,1,1,0,0,0,1,0] => 4
010 => [2,2] => [1,1,0,0,1,1,0,0] => 3
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 3
100 => [1,3] => [1,0,1,1,1,0,0,0] => 2
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 6
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 4
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 4
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 3
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 3
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 5
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 4
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 5
000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
>>> Load all 269 entries. <<<
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
111000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
111100 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
0000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
0000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
0000010 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 7
0001000 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 5
0001010 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5
0010001 => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
0011110 => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 4
0011111 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
0100000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
0100001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
0100011 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
0100111 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
0101111 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
0110000 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
0110001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
0110111 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3
0111000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
0111001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
0111100 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
0111101 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
0111110 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
0111111 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
1000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
1000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
1000010 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
1000011 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
1000100 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
1000111 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
1001110 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
1001111 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
1010000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
1011000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
1011100 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
1011110 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
1011111 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
1100000 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
1100001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
1100010 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
1100011 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
1100111 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
1101000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
1101100 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
1101111 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
1110000 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
1110001 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
1110010 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
1110011 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
1110100 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
1110110 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
1110111 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
1111000 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
1111001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
1111010 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
1111011 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
1111100 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
1111101 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
1111110 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1111111 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
00000000 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
00000001 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
00000010 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 8
00111111 => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
01000000 => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
01000001 => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
01111101 => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
01111110 => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
01111111 => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
10000000 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
10000001 => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
10000010 => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
10000011 => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
10011111 => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
10100000 => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
10111110 => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
11000000 => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
11000001 => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
11111010 => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
11111110 => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
000000000 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
000000001 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
000000010 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 9
001111111 => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
010000000 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
011111110 => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
011111111 => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
100000000 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2
100000001 => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
100000011 => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
110000000 => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
110000001 => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
111111110 => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1111111110 => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1100000001 => [1,1,8,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
1000000011 => [1,8,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
1000000000 => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 2
=> [1] => [1,0] => 2
0000000001 => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 11
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Description
The position of the first down step of a Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.
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.