Identifier
Values
0 => [2] => [1,1,0,0] => [2,1] => 1
1 => [1,1] => [1,0,1,0] => [1,2] => 0
00 => [3] => [1,1,1,0,0,0] => [3,2,1] => 0
01 => [2,1] => [1,1,0,0,1,0] => [2,1,3] => 1
10 => [1,2] => [1,0,1,1,0,0] => [1,3,2] => 1
11 => [1,1,1] => [1,0,1,0,1,0] => [1,2,3] => 0
000 => [4] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
001 => [3,1] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 0
010 => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 2
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 1
100 => [1,3] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 1
110 => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 0
0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 1
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 1
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 1
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 2
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 2
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 1
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 0
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 0
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 1
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 2
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 1
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 0
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 1
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 1
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 0
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 1
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 3
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 2
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 1
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 2
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 2
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 1
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 0
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 2
10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 2
10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 1
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 0
11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 2
11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 1
11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 1
11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 0
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => 0
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 1
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 1
000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 0
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => 1
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 0
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 1
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 1
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 1
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 0
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => 1
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => 1
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => 0
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 2
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => 1
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => 3
101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => 2
101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => 1
101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => 2
101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => 2
101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 1
110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 0
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 1
110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => 1
110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => 0
110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => 1
110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => 2
110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => 2
110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => 1
111000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 1
111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => 0
111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => 2
111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => 1
111100 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 1
111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 0
0000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => 1
0000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 0
>>> Load all 168 entries. <<<
0000010 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 2
0000011 => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => 1
0000100 => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 0
0000111 => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => 0
0001000 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 2
0001010 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 3
0001111 => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => 1
0010000 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 0
0011100 => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => 0
0011111 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => 0
0100000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 3
0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 3
0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 4
0111110 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 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] => [2,1,3,4,5,6,7,8] => 1
1000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 0
1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 0
1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 3
1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 2
1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 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] => [1,3,2,4,5,6,7,8] => 1
1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 2
1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 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] => [1,2,3,5,4,6,7,8] => 1
1111101 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 1
1111110 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1
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] => [1,2,3,4,5,6,7,8] => 0
00000000 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => 0
00000001 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => 1
00000011 => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => 0
00000111 => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => 1
00001111 => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => 0
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] => [4,3,2,1,5,6,7,8,9] => 1
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] => [3,2,1,4,5,6,7,8,9] => 0
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] => [2,1,3,4,5,6,7,8,9] => 1
10000000 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
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] => [1,2,3,4,5,6,7,9,8] => 1
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] => [1,2,3,4,5,6,7,8,9] => 0
000000000 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => 1
000000001 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => 0
000000010 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 2
000000011 => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => 1
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] => [7,6,5,4,3,2,1,8,9,10] => 0
000001000 => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 2
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] => [6,5,4,3,2,1,7,8,9,10] => 1
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] => [5,4,3,2,1,6,7,8,9,10] => 0
000100000 => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 2
000100010 => [4,4,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 3
000101000 => [4,2,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => 3
000101010 => [4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 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] => [4,3,2,1,5,6,7,8,9,10] => 1
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] => [3,2,1,4,5,6,7,8,9,10] => 0
010000000 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
010000010 => [2,6,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 3
010001000 => [2,4,4] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 3
010101000 => [2,2,2,4] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => 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] => [2,1,4,3,6,5,8,7,10,9] => 5
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] => [2,1,3,4,5,6,7,8,9,10] => 1
100000000 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 0
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] => [1,2,3,4,5,6,7,8,10,9] => 1
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] => [1,2,3,4,5,6,7,8,9,10] => 0
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] => [1,2,3,4,5,6,7,8,9,11,10] => 1
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] => [1,11,10,9,8,7,6,5,4,3,2] => 1
=> [1] => [1,0] => [1] => 0
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] => [10,9,8,7,6,5,4,3,2,1,11] => 1
01010101010 => [2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 6
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Description
The number of adjacent transpositions in the cycle decomposition of a permutation.
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.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
bounce path
Description
The bounce path determined by an integer composition.