Identifier
Values
[[1,2]] => 0 => [1] => [1,0] => 0
[[1],[2]] => 1 => [1] => [1,0] => 0
[[1,2,3]] => 00 => [2] => [1,1,0,0] => 0
[[1,3],[2]] => 10 => [1,1] => [1,0,1,0] => 1
[[1,2],[3]] => 01 => [1,1] => [1,0,1,0] => 1
[[1],[2],[3]] => 11 => [2] => [1,1,0,0] => 0
[[1,2,3,4]] => 000 => [3] => [1,1,1,0,0,0] => 0
[[1,3,4],[2]] => 100 => [1,2] => [1,0,1,1,0,0] => 2
[[1,2,3],[4]] => 001 => [2,1] => [1,1,0,0,1,0] => 1
[[1,4],[2],[3]] => 110 => [2,1] => [1,1,0,0,1,0] => 1
[[1,2],[3],[4]] => 011 => [1,2] => [1,0,1,1,0,0] => 2
[[1],[2],[3],[4]] => 111 => [3] => [1,1,1,0,0,0] => 0
[[1,2,3,4,5]] => 0000 => [4] => [1,1,1,1,0,0,0,0] => 0
[[1,3,4,5],[2]] => 1000 => [1,3] => [1,0,1,1,1,0,0,0] => 3
[[1,2,3,4],[5]] => 0001 => [3,1] => [1,1,1,0,0,0,1,0] => 1
[[1,3,4],[2,5]] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
[[1,4,5],[2],[3]] => 1100 => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,2,5],[3],[4]] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
[[1,3,4],[2],[5]] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
[[1,2,3],[4],[5]] => 0011 => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,2],[3,5],[4]] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
[[1,5],[2],[3],[4]] => 1110 => [3,1] => [1,1,1,0,0,0,1,0] => 1
[[1,2],[3],[4],[5]] => 0111 => [1,3] => [1,0,1,1,1,0,0,0] => 3
[[1],[2],[3],[4],[5]] => 1111 => [4] => [1,1,1,1,0,0,0,0] => 0
[[1,2,3,4,5,6]] => 00000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,4,5,6],[2]] => 10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,4,5],[6]] => 00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4,5],[2,6]] => 10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
[[1,4,5,6],[2],[3]] => 11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,2,5,6],[3],[4]] => 01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,6],[4],[5]] => 00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4,5],[2],[6]] => 10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
[[1,2,3,4],[5],[6]] => 00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,6],[3,5],[4]] => 01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
[[1,4,5],[2,6],[3]] => 11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3],[4,6],[5]] => 00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4],[2,5],[6]] => 10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
[[1,5,6],[2],[3],[4]] => 11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,6],[3],[4],[5]] => 01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
[[1,4,5],[2],[3],[6]] => 11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4],[2],[5],[6]] => 10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3],[4],[5],[6]] => 00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,2],[3,6],[4],[5]] => 01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
[[1,6],[2],[3],[4],[5]] => 11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2],[3],[4],[5],[6]] => 01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1],[2],[3],[4],[5],[6]] => 11111 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7]] => 000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,4,5,6,7],[2]] => 100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,2,3,4,5,6],[7]] => 000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,4,5,6],[2,7]] => 100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[1,4,5,6,7],[2],[3]] => 110000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,6,7],[3],[4]] => 011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,2,3,6,7],[4],[5]] => 001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,4,7],[5],[6]] => 000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[[1,3,4,5,6],[2],[7]] => 100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[1,2,3,4,5],[6],[7]] => 000011 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,6,7],[3,5],[4]] => 011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,2,3,7],[4,6],[5]] => 001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4,7],[2,5],[6]] => 100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,4,5,6],[2,7],[3]] => 110001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[[1,2,5,6],[3,7],[4]] => 011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,3,4],[5,7],[6]] => 000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[[1,3,4,5],[2,6],[7]] => 100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,5,6,7],[2],[3],[4]] => 111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,2,6,7],[3],[4],[5]] => 011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,3,4,7],[2],[5],[6]] => 100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,3,7],[4],[5],[6]] => 001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[[1,4,5,6],[2],[3],[7]] => 110001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[[1,2,5,6],[3],[4],[7]] => 011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4,5],[2],[6],[7]] => 100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,2,3,4],[5],[6],[7]] => 000111 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,2,6],[3,5,7],[4]] => 011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,3],[4,6,7],[5]] => 001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4],[2,5,7],[6]] => 100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,6],[3,5],[4,7]] => 011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,4,5],[2,6],[3,7]] => 110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4],[2,5],[6,7]] => 100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,7],[3,6],[4],[5]] => 011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,5,6],[2,7],[3],[4]] => 111001 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[[1,3,4],[2,7],[5],[6]] => 100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,3],[4,7],[5],[6]] => 001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[[1,2,6],[3,5],[4],[7]] => 011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,4,5],[2,6],[3],[7]] => 110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4],[2,5],[6],[7]] => 100111 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,6,7],[2],[3],[4],[5]] => 111100 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,7],[3],[4],[5],[6]] => 011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[1,5,6],[2],[3],[4],[7]] => 111001 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[[1,4,5],[2],[3],[6],[7]] => 110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4],[2],[5],[6],[7]] => 100111 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,2,3],[4],[5],[6],[7]] => 001111 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2],[3,7],[4],[5],[6]] => 011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[1,7],[2],[3],[4],[5],[6]] => 111110 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2],[3],[4],[5],[6],[7]] => 011111 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1],[2],[3],[4],[5],[6],[7]] => 111111 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7,8]] => 0000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,3,4,5,6,7,8],[2]] => 1000000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[[1,2,3,4,5,6,7],[8]] => 0000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,3,4,5,6,7],[2,8]] => 1000001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,4,5,6,7,8],[2],[3]] => 1100000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,2,5,6,7,8],[3],[4]] => 0110000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,2,3,6,7,8],[4],[5]] => 0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
>>> Load all 202 entries. <<<
[[1,2,3,4,7,8],[5],[6]] => 0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,4,5,8],[6],[7]] => 0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[[1,3,4,5,6,7],[2],[8]] => 1000001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,2,3,4,5,6],[7],[8]] => 0000011 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,6,7,8],[3,5],[4]] => 0110000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,2,3,7,8],[4,6],[5]] => 0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,3,4,7,8],[2,5],[6]] => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3,4,8],[5,7],[6]] => 0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4,5,8],[2,6],[7]] => 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,4,5,6,7],[2,8],[3]] => 1100001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[[1,2,5,6,7],[3,8],[4]] => 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,3,6,7],[4,8],[5]] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,3,4,5],[6,8],[7]] => 0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[[1,3,4,5,6],[2,7],[8]] => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[1,5,6,7,8],[2],[3],[4]] => 1110000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,6,7,8],[3],[4],[5]] => 0111000 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[[1,3,4,7,8],[2],[5],[6]] => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3,7,8],[4],[5],[6]] => 0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,3,4,5,8],[2],[6],[7]] => 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,2,3,4,8],[5],[6],[7]] => 0001110 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[[1,4,5,6,7],[2],[3],[8]] => 1100001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[[1,2,5,6,7],[3],[4],[8]] => 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,3,6,7],[4],[5],[8]] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4,5,6],[2],[7],[8]] => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[1,2,3,4,5],[6],[7],[8]] => 0000111 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[[1,2,3,8],[4,6,7],[5]] => 0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,3,4,8],[2,5,7],[6]] => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,6,7],[3,5,8],[4]] => 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,3,7],[4,6,8],[5]] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,3,4],[5,7,8],[6]] => 0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4,5],[2,6,8],[7]] => 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,4,5,8],[2,6],[3,7]] => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4,8],[2,5],[6,7]] => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,6,7],[3,5],[4,8]] => 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,3,7],[4,6],[5,8]] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,4,5,6],[2,7],[3,8]] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,2,5,6],[3,7],[4,8]] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,3,4,5],[2,6],[7,8]] => 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,2,7,8],[3,6],[4],[5]] => 0111000 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[[1,3,4,8],[2,7],[5],[6]] => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3,8],[4,7],[5],[6]] => 0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,4,5,8],[2,6],[3],[7]] => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4,8],[2,5],[6],[7]] => 1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,5,6,7],[2,8],[3],[4]] => 1110001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[[1,2,6,7],[3,8],[4],[5]] => 0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,3,4,5],[2,8],[6],[7]] => 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,2,3,4],[5,8],[6],[7]] => 0001110 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[[1,2,6,7],[3,5],[4],[8]] => 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,3,7],[4,6],[5],[8]] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,4,5,6],[2,7],[3],[8]] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,2,5,6],[3,7],[4],[8]] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,3,4,5],[2,6],[7],[8]] => 1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[[1,6,7,8],[2],[3],[4],[5]] => 1111000 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[[1,2,7,8],[3],[4],[5],[6]] => 0111100 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[1,4,5,8],[2],[3],[6],[7]] => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4,8],[2],[5],[6],[7]] => 1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,3,8],[4],[5],[6],[7]] => 0011110 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[[1,5,6,7],[2],[3],[4],[8]] => 1110001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[[1,2,6,7],[3],[4],[5],[8]] => 0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,4,5,6],[2],[3],[7],[8]] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,2,5,6],[3],[4],[7],[8]] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,3,4,5],[2],[6],[7],[8]] => 1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[[1,2,3,4],[5],[6],[7],[8]] => 0001111 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,4,5],[2,6,8],[3,7]] => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4],[2,5,8],[6,7]] => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,6],[3,5,7],[4,8]] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3],[4,6,7],[5,8]] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,7],[3,6,8],[4],[5]] => 0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,3,4],[2,7,8],[5],[6]] => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3],[4,7,8],[5],[6]] => 0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,4,5],[2,6,8],[3],[7]] => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4],[2,5,8],[6],[7]] => 1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,6],[3,5,7],[4],[8]] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3],[4,6,7],[5],[8]] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,2,7],[3,6],[4,8],[5]] => 0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,5,6],[2,7],[3,8],[4]] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[[1,4,5],[2,6],[3,8],[7]] => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4],[2,5],[6,8],[7]] => 1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,6],[3,5],[4,7],[8]] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,4,5],[2,6],[3,7],[8]] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,2,8],[3,7],[4],[5],[6]] => 0111100 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[1,6,7],[2,8],[3],[4],[5]] => 1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[[1,4,5],[2,8],[3],[6],[7]] => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[1,3,4],[2,8],[5],[6],[7]] => 1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[1,2,3],[4,8],[5],[6],[7]] => 0011110 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[[1,2,7],[3,6],[4],[5],[8]] => 0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[1,5,6],[2,7],[3],[4],[8]] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,6],[3,5],[4],[7],[8]] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,4,5],[2,6],[3],[7],[8]] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,3,4],[2,5],[6],[7],[8]] => 1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,8],[3],[4],[5],[6],[7]] => 0111110 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,6,7],[2],[3],[4],[5],[8]] => 1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[[1,5,6],[2],[3],[4],[7],[8]] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[[1,4,5],[2],[3],[6],[7],[8]] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[[1,3,4],[2],[5],[6],[7],[8]] => 1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,2,3],[4],[5],[6],[7],[8]] => 0011111 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,2],[3,8],[4],[5],[6],[7]] => 0111110 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2],[3],[4],[5],[6],[7],[8]] => 0111111 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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
bounce path
Description
The bounce path determined by an integer composition.
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 $w$.