Identifier
Values
0 => [2] => [1,1,0,0] => 0
1 => [1,1] => [1,0,1,0] => 1
00 => [3] => [1,1,1,0,0,0] => 0
01 => [2,1] => [1,1,0,0,1,0] => 2
10 => [1,2] => [1,0,1,1,0,0] => 1
11 => [1,1,1] => [1,0,1,0,1,0] => 3
000 => [4] => [1,1,1,1,0,0,0,0] => 0
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] => 5
100 => [1,3] => [1,0,1,1,1,0,0,0] => 1
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 3
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 6
0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
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] => 7
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 6
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 9
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 8
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] => 7
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 6
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 10
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
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] => 9
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] => 8
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 7
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 12
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 11
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 9
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 14
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 10
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 13
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 12
11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 11
11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 10
11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 15
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
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] => 11
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] => 10
000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 15
001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 14
001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 18
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 17
011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 20
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
>>> Load all 222 entries. <<<
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
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] => 10
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 19
110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
111000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
111100 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 21
0100000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
0100001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
0100011 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 15
0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
0100111 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
0101111 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 24
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] => 12
0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
0110111 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
0111000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
0111001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
0111100 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
0111101 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
0111110 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
0111111 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 27
1000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
1000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
1000010 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
1000011 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
1000100 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
1000111 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
1001110 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
1001111 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 23
1010000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
1011000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
1011100 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
1011110 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
1011111 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 26
1100000 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
1100001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
1100010 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
1100011 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
1100111 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
1101000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
1101100 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
1101111 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 25
1110000 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
1110001 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
1110010 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
1110011 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
1110100 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
1110110 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
1110111 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
1111000 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
1111001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
1111010 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
1111011 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
1111100 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
1111101 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
1111110 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
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] => 28
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Description
The major index east count of a Dyck path.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index east count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = E\}$.
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.