Identifier
Values
[[1,2]] => [1,2] => 0 => [1] => 1
[[1],[2]] => [2,1] => 1 => [1] => 1
[[1,2,3]] => [1,2,3] => 00 => [2] => 1
[[1,3],[2]] => [2,1,3] => 10 => [1,1] => 2
[[1,2],[3]] => [3,1,2] => 01 => [1,1] => 2
[[1],[2],[3]] => [3,2,1] => 11 => [2] => 1
[[1,2,3,4]] => [1,2,3,4] => 000 => [3] => 1
[[1,3,4],[2]] => [2,1,3,4] => 100 => [1,2] => 2
[[1,2,4],[3]] => [3,1,2,4] => 010 => [1,1,1] => 3
[[1,2,3],[4]] => [4,1,2,3] => 001 => [2,1] => 2
[[1,3],[2,4]] => [2,4,1,3] => 001 => [2,1] => 2
[[1,2],[3,4]] => [3,4,1,2] => 001 => [2,1] => 2
[[1,4],[2],[3]] => [3,2,1,4] => 110 => [2,1] => 2
[[1,3],[2],[4]] => [4,2,1,3] => 101 => [1,1,1] => 3
[[1,2],[3],[4]] => [4,3,1,2] => 011 => [1,2] => 2
[[1],[2],[3],[4]] => [4,3,2,1] => 111 => [3] => 1
[[1,2,3,4,5]] => [1,2,3,4,5] => 0000 => [4] => 1
[[1,3,4,5],[2]] => [2,1,3,4,5] => 1000 => [1,3] => 2
[[1,2,4,5],[3]] => [3,1,2,4,5] => 0100 => [1,1,2] => 3
[[1,2,3,5],[4]] => [4,1,2,3,5] => 0010 => [2,1,1] => 3
[[1,2,3,4],[5]] => [5,1,2,3,4] => 0001 => [3,1] => 2
[[1,3,5],[2,4]] => [2,4,1,3,5] => 0010 => [2,1,1] => 3
[[1,2,5],[3,4]] => [3,4,1,2,5] => 0010 => [2,1,1] => 3
[[1,3,4],[2,5]] => [2,5,1,3,4] => 0001 => [3,1] => 2
[[1,2,4],[3,5]] => [3,5,1,2,4] => 0001 => [3,1] => 2
[[1,2,3],[4,5]] => [4,5,1,2,3] => 0001 => [3,1] => 2
[[1,4,5],[2],[3]] => [3,2,1,4,5] => 1100 => [2,2] => 2
[[1,3,5],[2],[4]] => [4,2,1,3,5] => 1010 => [1,1,1,1] => 4
[[1,2,5],[3],[4]] => [4,3,1,2,5] => 0110 => [1,2,1] => 2
[[1,3,4],[2],[5]] => [5,2,1,3,4] => 1001 => [1,2,1] => 2
[[1,2,4],[3],[5]] => [5,3,1,2,4] => 0101 => [1,1,1,1] => 4
[[1,2,3],[4],[5]] => [5,4,1,2,3] => 0011 => [2,2] => 2
[[1,4],[2,5],[3]] => [3,2,5,1,4] => 0101 => [1,1,1,1] => 4
[[1,3],[2,5],[4]] => [4,2,5,1,3] => 0011 => [2,2] => 2
[[1,2],[3,5],[4]] => [4,3,5,1,2] => 0011 => [2,2] => 2
[[1,3],[2,4],[5]] => [5,2,4,1,3] => 0011 => [2,2] => 2
[[1,2],[3,4],[5]] => [5,3,4,1,2] => 0011 => [2,2] => 2
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => 1110 => [3,1] => 2
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => 1101 => [2,1,1] => 3
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => 1011 => [1,1,2] => 3
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => 0111 => [1,3] => 2
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 1111 => [4] => 1
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 00000 => [5] => 1
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => 10000 => [1,4] => 2
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => 01000 => [1,1,3] => 3
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => 00100 => [2,1,2] => 3
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => 00010 => [3,1,1] => 3
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 00001 => [4,1] => 2
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 00100 => [2,1,2] => 3
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 00100 => [2,1,2] => 3
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 00010 => [3,1,1] => 3
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 00010 => [3,1,1] => 3
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 00010 => [3,1,1] => 3
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 00001 => [4,1] => 2
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 00001 => [4,1] => 2
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 00001 => [4,1] => 2
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 00001 => [4,1] => 2
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 11000 => [2,3] => 2
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 10100 => [1,1,1,2] => 4
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 01100 => [1,2,2] => 2
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 10010 => [1,2,1,1] => 3
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 01010 => [1,1,1,1,1] => 5
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 00110 => [2,2,1] => 2
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 10001 => [1,3,1] => 2
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 01001 => [1,1,2,1] => 3
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 00101 => [2,1,1,1] => 4
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 00011 => [3,2] => 2
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 00001 => [4,1] => 2
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 00001 => [4,1] => 2
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 00001 => [4,1] => 2
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 00001 => [4,1] => 2
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 00001 => [4,1] => 2
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 01010 => [1,1,1,1,1] => 5
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 00110 => [2,2,1] => 2
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 00110 => [2,2,1] => 2
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 00110 => [2,2,1] => 2
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 00110 => [2,2,1] => 2
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 01001 => [1,1,2,1] => 3
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 00101 => [2,1,1,1] => 4
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 00101 => [2,1,1,1] => 4
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 00011 => [3,2] => 2
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 00011 => [3,2] => 2
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 00011 => [3,2] => 2
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 00101 => [2,1,1,1] => 4
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 00101 => [2,1,1,1] => 4
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 00011 => [3,2] => 2
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 00011 => [3,2] => 2
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 00011 => [3,2] => 2
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 11100 => [3,2] => 2
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 11010 => [2,1,1,1] => 4
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 10110 => [1,1,2,1] => 3
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 01110 => [1,3,1] => 2
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 11001 => [2,2,1] => 2
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 10101 => [1,1,1,1,1] => 5
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 01101 => [1,2,1,1] => 3
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 10011 => [1,2,2] => 2
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 01011 => [1,1,1,2] => 4
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 00111 => [2,3] => 2
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 00011 => [3,2] => 2
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 00011 => [3,2] => 2
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 00011 => [3,2] => 2
>>> Load all 350 entries. <<<
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 00101 => [2,1,1,1] => 4
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 00101 => [2,1,1,1] => 4
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 01101 => [1,2,1,1] => 3
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 01011 => [1,1,1,2] => 4
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 00111 => [2,3] => 2
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 00111 => [2,3] => 2
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 01011 => [1,1,1,2] => 4
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 00111 => [2,3] => 2
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 00111 => [2,3] => 2
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 00111 => [2,3] => 2
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 00111 => [2,3] => 2
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => 11110 => [4,1] => 2
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => 11101 => [3,1,1] => 3
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => 11011 => [2,1,2] => 3
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => 10111 => [1,1,3] => 3
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 01111 => [1,4] => 2
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 11111 => [5] => 1
[[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 000000 => [6] => 1
[[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => 100000 => [1,5] => 2
[[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => 010000 => [1,1,4] => 3
[[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => 001000 => [2,1,3] => 3
[[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => 000100 => [3,1,2] => 3
[[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => 000010 => [4,1,1] => 3
[[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 000001 => [5,1] => 2
[[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => 001000 => [2,1,3] => 3
[[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => 001000 => [2,1,3] => 3
[[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => 000100 => [3,1,2] => 3
[[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => 000100 => [3,1,2] => 3
[[1,2,3,6,7],[4,5]] => [4,5,1,2,3,6,7] => 000100 => [3,1,2] => 3
[[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => 000010 => [4,1,1] => 3
[[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => 000010 => [4,1,1] => 3
[[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => 000010 => [4,1,1] => 3
[[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => 000010 => [4,1,1] => 3
[[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => 000001 => [5,1] => 2
[[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => 000001 => [5,1] => 2
[[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => 000001 => [5,1] => 2
[[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => 000001 => [5,1] => 2
[[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 000001 => [5,1] => 2
[[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => 110000 => [2,4] => 2
[[1,3,5,6,7],[2],[4]] => [4,2,1,3,5,6,7] => 101000 => [1,1,1,3] => 4
[[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => 011000 => [1,2,3] => 2
[[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => 100100 => [1,2,1,2] => 3
[[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => 010100 => [1,1,1,1,2] => 5
[[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => 001100 => [2,2,2] => 2
[[1,3,4,5,7],[2],[6]] => [6,2,1,3,4,5,7] => 100010 => [1,3,1,1] => 3
[[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => 010010 => [1,1,2,1,1] => 3
[[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => 001010 => [2,1,1,1,1] => 5
[[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => 000110 => [3,2,1] => 2
[[1,3,4,5,6],[2],[7]] => [7,2,1,3,4,5,6] => 100001 => [1,4,1] => 2
[[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => 010001 => [1,1,3,1] => 3
[[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => 001001 => [2,1,2,1] => 3
[[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => 000101 => [3,1,1,1] => 4
[[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 000011 => [4,2] => 2
[[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => 000010 => [4,1,1] => 3
[[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => 000010 => [4,1,1] => 3
[[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => 000010 => [4,1,1] => 3
[[1,2,4,7],[3,5,6]] => [3,5,6,1,2,4,7] => 000010 => [4,1,1] => 3
[[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => 000010 => [4,1,1] => 3
[[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => 000001 => [5,1] => 2
[[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => 000001 => [5,1] => 2
[[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => 000001 => [5,1] => 2
[[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => 000001 => [5,1] => 2
[[1,2,3,6],[4,5,7]] => [4,5,7,1,2,3,6] => 000001 => [5,1] => 2
[[1,3,4,5],[2,6,7]] => [2,6,7,1,3,4,5] => 000001 => [5,1] => 2
[[1,2,4,5],[3,6,7]] => [3,6,7,1,2,4,5] => 000001 => [5,1] => 2
[[1,2,3,5],[4,6,7]] => [4,6,7,1,2,3,5] => 000001 => [5,1] => 2
[[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 000001 => [5,1] => 2
[[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => 010100 => [1,1,1,1,2] => 5
[[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => 001100 => [2,2,2] => 2
[[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => 001100 => [2,2,2] => 2
[[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => 001100 => [2,2,2] => 2
[[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => 001100 => [2,2,2] => 2
[[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => 010010 => [1,1,2,1,1] => 3
[[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => 001010 => [2,1,1,1,1] => 5
[[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => 001010 => [2,1,1,1,1] => 5
[[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => 000110 => [3,2,1] => 2
[[1,2,4,7],[3,6],[5]] => [5,3,6,1,2,4,7] => 000110 => [3,2,1] => 2
[[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => 000110 => [3,2,1] => 2
[[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => 001010 => [2,1,1,1,1] => 5
[[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => 001010 => [2,1,1,1,1] => 5
[[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => 000110 => [3,2,1] => 2
[[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => 000110 => [3,2,1] => 2
[[1,2,3,7],[4,5],[6]] => [6,4,5,1,2,3,7] => 000110 => [3,2,1] => 2
[[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => 010001 => [1,1,3,1] => 3
[[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => 001001 => [2,1,2,1] => 3
[[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => 001001 => [2,1,2,1] => 3
[[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => 000101 => [3,1,1,1] => 4
[[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => 000101 => [3,1,1,1] => 4
[[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => 000101 => [3,1,1,1] => 4
[[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => 000011 => [4,2] => 2
[[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => 000011 => [4,2] => 2
[[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => 000011 => [4,2] => 2
[[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => 000011 => [4,2] => 2
[[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => 001001 => [2,1,2,1] => 3
[[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => 001001 => [2,1,2,1] => 3
[[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => 000101 => [3,1,1,1] => 4
[[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => 000101 => [3,1,1,1] => 4
[[1,2,3,6],[4,5],[7]] => [7,4,5,1,2,3,6] => 000101 => [3,1,1,1] => 4
[[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => 000011 => [4,2] => 2
[[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => 000011 => [4,2] => 2
[[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => 000011 => [4,2] => 2
[[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 000011 => [4,2] => 2
[[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => 111000 => [3,3] => 2
[[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => 110100 => [2,1,1,2] => 4
[[1,3,6,7],[2],[4],[5]] => [5,4,2,1,3,6,7] => 101100 => [1,1,2,2] => 3
[[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => 011100 => [1,3,2] => 2
[[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => 110010 => [2,2,1,1] => 3
[[1,3,5,7],[2],[4],[6]] => [6,4,2,1,3,5,7] => 101010 => [1,1,1,1,1,1] => 6
[[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => 011010 => [1,2,1,1,1] => 4
[[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => 100110 => [1,2,2,1] => 2
[[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => 010110 => [1,1,1,2,1] => 4
[[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => 001110 => [2,3,1] => 2
[[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => 110001 => [2,3,1] => 2
[[1,3,5,6],[2],[4],[7]] => [7,4,2,1,3,5,6] => 101001 => [1,1,1,2,1] => 4
[[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => 011001 => [1,2,2,1] => 2
[[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => 100101 => [1,2,1,1,1] => 4
[[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => 010101 => [1,1,1,1,1,1] => 6
[[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => 001101 => [2,2,1,1] => 3
[[1,3,4,5],[2],[6],[7]] => [7,6,2,1,3,4,5] => 100011 => [1,3,2] => 2
[[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => 010011 => [1,1,2,2] => 3
[[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => 001011 => [2,1,1,2] => 4
[[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 000111 => [3,3] => 2
[[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => 010001 => [1,1,3,1] => 3
[[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => 001001 => [2,1,2,1] => 3
[[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => 001001 => [2,1,2,1] => 3
[[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => 000101 => [3,1,1,1] => 4
[[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => 000101 => [3,1,1,1] => 4
[[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => 010001 => [1,1,3,1] => 3
[[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => 001001 => [2,1,2,1] => 3
[[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => 001001 => [2,1,2,1] => 3
[[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => 000101 => [3,1,1,1] => 4
[[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => 000101 => [3,1,1,1] => 4
[[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => 000101 => [3,1,1,1] => 4
[[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => 000011 => [4,2] => 2
[[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => 000011 => [4,2] => 2
[[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => 000011 => [4,2] => 2
[[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => 000011 => [4,2] => 2
[[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => 000011 => [4,2] => 2
[[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => 000011 => [4,2] => 2
[[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => 000011 => [4,2] => 2
[[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => 000011 => [4,2] => 2
[[1,2,4],[3,5,6],[7]] => [7,3,5,6,1,2,4] => 000011 => [4,2] => 2
[[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 000011 => [4,2] => 2
[[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => 000110 => [3,2,1] => 2
[[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => 000110 => [3,2,1] => 2
[[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => 000110 => [3,2,1] => 2
[[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => 001010 => [2,1,1,1,1] => 5
[[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => 001010 => [2,1,1,1,1] => 5
[[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => 000101 => [3,1,1,1] => 4
[[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => 000101 => [3,1,1,1] => 4
[[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => 000101 => [3,1,1,1] => 4
[[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => 001001 => [2,1,2,1] => 3
[[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => 001001 => [2,1,2,1] => 3
[[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => 000011 => [4,2] => 2
[[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => 000011 => [4,2] => 2
[[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => 000011 => [4,2] => 2
[[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => 000011 => [4,2] => 2
[[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => 000011 => [4,2] => 2
[[1,2,3],[4,6],[5,7]] => [5,7,4,6,1,2,3] => 000011 => [4,2] => 2
[[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => 001001 => [2,1,2,1] => 3
[[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => 001001 => [2,1,2,1] => 3
[[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => 000101 => [3,1,1,1] => 4
[[1,2,4],[3,5],[6,7]] => [6,7,3,5,1,2,4] => 000101 => [3,1,1,1] => 4
[[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 000101 => [3,1,1,1] => 4
[[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => 011010 => [1,2,1,1,1] => 4
[[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => 010110 => [1,1,1,2,1] => 4
[[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => 001110 => [2,3,1] => 2
[[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => 001110 => [2,3,1] => 2
[[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => 010110 => [1,1,1,2,1] => 4
[[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => 001110 => [2,3,1] => 2
[[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => 001110 => [2,3,1] => 2
[[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => 001110 => [2,3,1] => 2
[[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => 001110 => [2,3,1] => 2
[[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => 011001 => [1,2,2,1] => 2
[[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => 010101 => [1,1,1,1,1,1] => 6
[[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => 001101 => [2,2,1,1] => 3
[[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => 001101 => [2,2,1,1] => 3
[[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => 010011 => [1,1,2,2] => 3
[[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => 001011 => [2,1,1,2] => 4
[[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => 001011 => [2,1,1,2] => 4
[[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => 000111 => [3,3] => 2
[[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => 000111 => [3,3] => 2
[[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => 000111 => [3,3] => 2
[[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => 010101 => [1,1,1,1,1,1] => 6
[[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => 001101 => [2,2,1,1] => 3
[[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => 001101 => [2,2,1,1] => 3
[[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => 001101 => [2,2,1,1] => 3
[[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => 001101 => [2,2,1,1] => 3
[[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => 010011 => [1,1,2,2] => 3
[[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => 001011 => [2,1,1,2] => 4
[[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => 001011 => [2,1,1,2] => 4
[[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => 000111 => [3,3] => 2
[[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => 000111 => [3,3] => 2
[[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => 000111 => [3,3] => 2
[[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => 001011 => [2,1,1,2] => 4
[[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => 001011 => [2,1,1,2] => 4
[[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => 000111 => [3,3] => 2
[[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => 000111 => [3,3] => 2
[[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 000111 => [3,3] => 2
[[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => 111100 => [4,2] => 2
[[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => 111010 => [3,1,1,1] => 4
[[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => 110110 => [2,1,2,1] => 3
[[1,3,7],[2],[4],[5],[6]] => [6,5,4,2,1,3,7] => 101110 => [1,1,3,1] => 3
[[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => 011110 => [1,4,1] => 2
[[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => 111001 => [3,2,1] => 2
[[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => 110101 => [2,1,1,1,1] => 5
[[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => 101101 => [1,1,2,1,1] => 3
[[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => 011101 => [1,3,1,1] => 3
[[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => 110011 => [2,2,2] => 2
[[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => 101011 => [1,1,1,1,2] => 5
[[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => 011011 => [1,2,1,2] => 3
[[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => 100111 => [1,2,3] => 2
[[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => 010111 => [1,1,1,3] => 4
[[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 001111 => [2,4] => 2
[[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => 001011 => [2,1,1,2] => 4
[[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => 000111 => [3,3] => 2
[[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => 000111 => [3,3] => 2
[[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => 000111 => [3,3] => 2
[[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => 000111 => [3,3] => 2
[[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => 000111 => [3,3] => 2
[[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => 000111 => [3,3] => 2
[[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => 001011 => [2,1,1,2] => 4
[[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => 001011 => [2,1,1,2] => 4
[[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => 000111 => [3,3] => 2
[[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => 000111 => [3,3] => 2
[[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => 000111 => [3,3] => 2
[[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => 001011 => [2,1,1,2] => 4
[[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 001011 => [2,1,1,2] => 4
[[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => 011101 => [1,3,1,1] => 3
[[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => 011011 => [1,2,1,2] => 3
[[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => 010111 => [1,1,1,3] => 4
[[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => 001111 => [2,4] => 2
[[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => 001111 => [2,4] => 2
[[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => 011011 => [1,2,1,2] => 3
[[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => 010111 => [1,1,1,3] => 4
[[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => 001111 => [2,4] => 2
[[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => 001111 => [2,4] => 2
[[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => 010111 => [1,1,1,3] => 4
[[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => 001111 => [2,4] => 2
[[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => 001111 => [2,4] => 2
[[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => 001111 => [2,4] => 2
[[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 001111 => [2,4] => 2
[[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => 111110 => [5,1] => 2
[[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => 111101 => [4,1,1] => 3
[[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => 111011 => [3,1,2] => 3
[[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => 110111 => [2,1,3] => 3
[[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => 101111 => [1,1,4] => 3
[[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 011111 => [1,5] => 2
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 111111 => [6] => 1
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Description
The global dimension of the corresponding Comp-Nakayama algebra.
We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.