Identifier
Values
[1,0] => [[1],[2]] => 1 => 1 => 1
[1,0,1,0] => [[1,3],[2,4]] => 101 => 110 => 2
[1,1,0,0] => [[1,2],[3,4]] => 010 => 101 => 2
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 10101 => 11010 => 3
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => 10010 => 10101 => 3
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => 01001 => 10010 => 2
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => 01010 => 10101 => 3
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => 00100 => 01001 => 2
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 1010101 => 1101010 => 4
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 1010010 => 1100101 => 4
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 1001001 => 1010010 => 3
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 1001010 => 1010101 => 4
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 1000100 => 1001001 => 3
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0100101 => 1001010 => 3
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 0100010 => 1000101 => 3
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 0101001 => 1010010 => 3
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => 0101010 => 1010101 => 4
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 0100100 => 1001001 => 3
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 0010001 => 0100010 => 2
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 0010010 => 0100101 => 3
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 0010100 => 0101001 => 3
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 0010001 => 2
[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 101010101 => 110101010 => 5
[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 101001001 => 110010010 => 4
[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 100100101 => 101001010 => 4
[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 100101001 => 101010010 => 4
[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 100101010 => 101010101 => 5
[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 100100100 => 101001001 => 4
[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => 100010001 => 100100010 => 3
[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => 100010010 => 100100101 => 4
[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => 100010100 => 100101001 => 4
[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => 100001000 => 100010001 => 3
[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 010010101 => 100101010 => 4
[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => 010010010 => 100100101 => 4
[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => 010001001 => 100010010 => 3
[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 010100101 => 101001010 => 4
[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 010101001 => 101010010 => 4
[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => 010101010 => 101010101 => 5
[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => 010100100 => 101001001 => 4
[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => 010010001 => 100100010 => 3
[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => 010010010 => 100100101 => 4
[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => 010010100 => 100101001 => 4
[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => 010001000 => 100010001 => 3
[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => 001000101 => 010001010 => 3
[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => 001000010 => 010000101 => 3
[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => 001001001 => 010010010 => 3
[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => 001001010 => 010010101 => 4
[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => 001000100 => 010001001 => 3
[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => 001010001 => 010100010 => 3
[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => 001010010 => 010100101 => 4
[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => 001010100 => 010101001 => 4
[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => 001001000 => 010010001 => 3
[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => 000100001 => 001000010 => 2
[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => 000100010 => 001000101 => 3
[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => 000100100 => 001001001 => 3
[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => 000101000 => 001010001 => 3
[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 000100001 => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => 10010010101 => 10100101010 => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => 10010010010 => 10100100101 => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => 10010001001 => 10100010010 => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => 10010100101 => 10101001010 => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 10010101001 => 10101010010 => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => 10010101010 => 10101010101 => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 10010100100 => 10101001001 => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => 10010010001 => 10100100010 => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 10010010010 => 10100100101 => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 10010010100 => 10100101001 => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 10010001000 => 10100010001 => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 10001000101 => 10010001010 => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => 10001001001 => 10010010010 => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 10001001010 => 10010010101 => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 10001000100 => 10010001001 => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 10001010001 => 10010100010 => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 10001010010 => 10010100101 => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 10001010100 => 10010101001 => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 10001001000 => 10010010001 => 4
[1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 10000100001 => 10001000010 => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 10000100010 => 10001000101 => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 10000100100 => 10001001001 => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 10000101000 => 10001010001 => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => 10000010000 => 10000100001 => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => 01001010101 => 10010101010 => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => 01001010010 => 10010100101 => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => 01001001001 => 10010010010 => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 01001001010 => 10010010101 => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => 01001000100 => 10010001001 => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => 01000100101 => 10001001010 => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 01000100010 => 10001000101 => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 01000101001 => 10001010010 => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 01000100100 => 10001001001 => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => 01000010001 => 10000100010 => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => 01010010101 => 10100101010 => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 01010010010 => 10100100101 => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 01010001001 => 10100010010 => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 01010100101 => 10101001010 => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => 01010101001 => 10101010010 => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => 01010101010 => 10101010101 => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => 01010100100 => 10101001001 => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 01010010001 => 10100100010 => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => 01010010010 => 10100100101 => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => 01010010100 => 10100101001 => 5
>>> Load all 159 entries. <<<
[1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => 01010001000 => 10100010001 => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => 01001000101 => 10010001010 => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 01001001001 => 10010010010 => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => 01001001010 => 10010010101 => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => 01001000100 => 10010001001 => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 01001010001 => 10010100010 => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => 01001010010 => 10010100101 => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => 01001010100 => 10010101001 => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => 01001001000 => 10010010001 => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 01000100001 => 10001000010 => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => 01000100010 => 10001000101 => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => 01000100100 => 10001001001 => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => 01000101000 => 10001010001 => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => 01000010000 => 10000100001 => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 00100010101 => 01000101010 => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => 00100010010 => 01000100101 => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => 00100001001 => 01000010010 => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => 00100100101 => 01001001010 => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => 00100100010 => 01001000101 => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 00100101001 => 01001010010 => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => 00100101010 => 01001010101 => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => 00100100100 => 01001001001 => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => 00100010001 => 01000100010 => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => 00100010010 => 01000100101 => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => 00100010100 => 01000101001 => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => 00100001000 => 01000010001 => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 00101000101 => 01010001010 => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 00101001001 => 01010010010 => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => 00101001010 => 01010010101 => 5
[1,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => 00101000100 => 01010001001 => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 00101010001 => 01010100010 => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => 00101010010 => 01010100101 => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => 00101010100 => 01010101001 => 5
[1,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => 00101001000 => 01010010001 => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => 00100100001 => 01001000010 => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => 00100100010 => 01001000101 => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => 00100100100 => 01001001001 => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => 00100101000 => 01001010001 => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => 00100010000 => 01000100001 => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => 00010000101 => 00100001010 => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => 00010001001 => 00100010010 => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => 00010001010 => 00100010101 => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => 00010000100 => 00100001001 => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => 00010010001 => 00100100010 => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => 00010010010 => 00100100101 => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => 00010010100 => 00100101001 => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => 00010001000 => 00100010001 => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => 00010100001 => 00101000010 => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => 00010100010 => 00101000101 => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => 00010100100 => 00101001001 => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => 00010101000 => 00101010001 => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => 00010010000 => 00100100001 => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 00001000001 => 00010000010 => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => 00001000010 => 00010000101 => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => 00001000100 => 00010001001 => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => 00001001000 => 00010010001 => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => 00001010000 => 00010100001 => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000 => 00001000001 => 2
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Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Map
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.