Identifier
Values
0 => [2] => [1,1,0,0] => 2
1 => [1,1] => [1,0,1,0] => 1
00 => [3] => [1,1,1,0,0,0] => 3
01 => [2,1] => [1,1,0,0,1,0] => 2
10 => [1,2] => [1,0,1,1,0,0] => 2
11 => [1,1,1] => [1,0,1,0,1,0] => 1
000 => [4] => [1,1,1,1,0,0,0,0] => 4
001 => [3,1] => [1,1,1,0,0,0,1,0] => 3
010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
100 => [1,3] => [1,0,1,1,1,0,0,0] => 3
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] => 1
0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
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] => 2
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
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] => 3
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] => 1
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
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] => 2
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
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] => 2
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
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] => 4
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
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] => 3
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] => 1
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
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] => 3
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
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] => 2
010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
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] => 2
011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
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] => 2
011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
>>> Load all 350 entries. <<<
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
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] => 3
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] => 5
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
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] => 4
111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
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] => 3
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] => 1
0000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
0000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
0000010 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
0000011 => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
0000100 => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 5
0000111 => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 5
0001000 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
0001010 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
0001011 => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 4
0001101 => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 4
0001110 => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 4
0001111 => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
0010000 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
0010001 => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
0010011 => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 3
0010101 => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 3
0010110 => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 3
0011001 => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 3
0011010 => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 3
0011100 => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 3
0011110 => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
0011111 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
0100000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
0100001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
0100011 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
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] => 4
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] => 2
0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
0101111 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
0110000 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
0110001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
0111000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
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] => 2
0111110 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0111111 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
1000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
1000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
1000010 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
1000011 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
1001111 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
1010000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
1011000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
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] => 6
1100001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
1100010 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
1100111 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
1101000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 5
1110010 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
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] => 4
1111001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
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] => 3
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] => 1
00000000 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
00000001 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
00000010 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 7
00000011 => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 7
00000100 => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 6
00000111 => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 6
00001000 => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 5
00001111 => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
00010000 => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
00010011 => [4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => 4
00010101 => [4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => 4
00010110 => [4,2,1,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0] => 4
00011001 => [4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => 4
00011010 => [4,1,2,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0] => 4
00011100 => [4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => 4
00011111 => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
00100000 => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
00100011 => [3,4,1,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
00100101 => [3,3,2,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
00100110 => [3,3,1,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
00101001 => [3,2,3,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
00101010 => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
00101100 => [3,2,1,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
00110001 => [3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
00110010 => [3,1,3,2] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
00110100 => [3,1,2,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
00111000 => [3,1,1,4] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
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] => 3
01000000 => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
01000001 => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
01000101 => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
01000110 => [2,4,1,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
01001001 => [2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
01001100 => [2,3,1,3] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
01010001 => [2,2,4,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
01010101 => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
01011000 => [2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
01011111 => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
01100010 => [2,1,4,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
01100100 => [2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
01101000 => [2,1,2,4] => [1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
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] => 2
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] => 2
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] => 2
10000000 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
10000001 => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
10000010 => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
10000011 => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
10001001 => [1,4,3,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
10001010 => [1,4,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
10001100 => [1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 4
10010001 => [1,3,4,1] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
10010010 => [1,3,3,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 3
10010100 => [1,3,2,3] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 3
10011000 => [1,3,1,4] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 4
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] => 3
10100000 => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
10100010 => [1,2,4,2] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
10100100 => [1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
10101000 => [1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
10101010 => [1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
10101111 => [1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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
10111111 => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
11000000 => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
11000001 => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
11000100 => [1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
11001000 => [1,1,3,4] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
11001010 => [1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
11011111 => [1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
11100000 => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
11101010 => [1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
11101111 => [1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
11110010 => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
11111000 => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
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
11111100 => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
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
11111111 => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
000000000 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
000000001 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 9
000000010 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 8
000000011 => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 8
000000100 => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 7
000000111 => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 7
000001000 => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 6
000001111 => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 6
000010000 => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
000011111 => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
000100000 => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
000100101 => [4,3,2,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
000100110 => [4,3,1,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
000101001 => [4,2,3,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
000101100 => [4,2,1,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
000110010 => [4,1,3,2] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
000110100 => [4,1,2,3] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
000111111 => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
001000000 => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
001000101 => [3,4,2,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
001000110 => [3,4,1,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
001010001 => [3,2,4,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
001011000 => [3,2,1,4] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
001100010 => [3,1,4,2] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
001101000 => [3,1,2,4] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
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] => 3
010000000 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
010001001 => [2,4,3,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
010001100 => [2,4,1,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 4
010010001 => [2,3,4,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
010011000 => [2,3,1,4] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 4
010101010 => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
011000100 => [2,1,4,3] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
011001000 => [2,1,3,4] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
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] => 2
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] => 2
100000000 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
100000001 => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
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] => 7
100010010 => [1,4,3,2] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => 4
100010100 => [1,4,2,3] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => 4
100100010 => [1,3,4,2] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
100101000 => [1,3,2,4] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
101000100 => [1,2,4,3] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
101001000 => [1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
101010101 => [1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 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] => 8
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] => 7
110101010 => [1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
111101010 => [1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
111110111 => [1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
111111010 => [1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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
111111111 => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
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] => 8
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] => 8
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] => 10
=> [1] => [1,0] => 1
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] => 10
11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
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Description
The height of a Dyck path.
The height of a Dyck path $D$ of semilength $n$ is defined as the maximal height of a peak of $D$. The height of $D$ at position $i$ is the number of up-steps minus the number of down-steps before position $i$.
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.