Processing math: 100%

Identifier
Values
[[1,2]] => [2] => [1,0,1,0] => 1010 => 1
[[2,2]] => [2] => [1,0,1,0] => 1010 => 1
[[1],[2]] => [1,1] => [1,1,0,0] => 1100 => 1
[[1,3]] => [2] => [1,0,1,0] => 1010 => 1
[[2,3]] => [2] => [1,0,1,0] => 1010 => 1
[[3,3]] => [2] => [1,0,1,0] => 1010 => 1
[[1],[3]] => [1,1] => [1,1,0,0] => 1100 => 1
[[2],[3]] => [1,1] => [1,1,0,0] => 1100 => 1
[[1,1,2]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,2,2]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,2,2]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,1],[2]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,2],[2]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,4]] => [2] => [1,0,1,0] => 1010 => 1
[[2,4]] => [2] => [1,0,1,0] => 1010 => 1
[[3,4]] => [2] => [1,0,1,0] => 1010 => 1
[[4,4]] => [2] => [1,0,1,0] => 1010 => 1
[[1],[4]] => [1,1] => [1,1,0,0] => 1100 => 1
[[2],[4]] => [1,1] => [1,1,0,0] => 1100 => 1
[[3],[4]] => [1,1] => [1,1,0,0] => 1100 => 1
[[1,1,3]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,2,3]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,3,3]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,2,3]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,3,3]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,3,3]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,1],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,2],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,3],[2]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,3],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,2],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,3],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1],[2],[3]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,5]] => [2] => [1,0,1,0] => 1010 => 1
[[2,5]] => [2] => [1,0,1,0] => 1010 => 1
[[3,5]] => [2] => [1,0,1,0] => 1010 => 1
[[4,5]] => [2] => [1,0,1,0] => 1010 => 1
[[5,5]] => [2] => [1,0,1,0] => 1010 => 1
[[1],[5]] => [1,1] => [1,1,0,0] => 1100 => 1
[[2],[5]] => [1,1] => [1,1,0,0] => 1100 => 1
[[3],[5]] => [1,1] => [1,1,0,0] => 1100 => 1
[[4],[5]] => [1,1] => [1,1,0,0] => 1100 => 1
[[1,1,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,2,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,3,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,4,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,2,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,3,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,4,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,3,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,4,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,4,4]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,1],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,2],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,4],[2]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,3],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,4],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,4],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,2],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,3],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,4],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,4],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,3],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,4],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1],[2],[4]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[3],[4]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[3],[4]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1,1],[2,3]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[3,3]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[2,3]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[3,3]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[3,3]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,6]] => [2] => [1,0,1,0] => 1010 => 1
[[2,6]] => [2] => [1,0,1,0] => 1010 => 1
[[3,6]] => [2] => [1,0,1,0] => 1010 => 1
[[4,6]] => [2] => [1,0,1,0] => 1010 => 1
[[5,6]] => [2] => [1,0,1,0] => 1010 => 1
[[6,6]] => [2] => [1,0,1,0] => 1010 => 1
[[1],[6]] => [1,1] => [1,1,0,0] => 1100 => 1
[[2],[6]] => [1,1] => [1,1,0,0] => 1100 => 1
[[3],[6]] => [1,1] => [1,1,0,0] => 1100 => 1
[[4],[6]] => [1,1] => [1,1,0,0] => 1100 => 1
[[5],[6]] => [1,1] => [1,1,0,0] => 1100 => 1
[[1,1,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,2,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,3,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,4,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,5,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,2,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,3,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,4,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,5,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,3,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,4,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,5,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,4,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,5,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[5,5,5]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,1],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,2],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
>>> Load all 406 entries. <<<
[[1,5],[2]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,3],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,5],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,4],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,5],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,5],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,2],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,3],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,5],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,4],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,5],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,5],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,3],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,4],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,5],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,5],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,4],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,5],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1],[2],[5]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[3],[5]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[4],[5]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[3],[5]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[4],[5]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[3],[4],[5]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1,1],[2,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[3,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[4,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[2,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[3,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[2,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[4,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[3,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[4,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[3,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[4,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[3,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[4,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,3],[4,4]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,7]] => [2] => [1,0,1,0] => 1010 => 1
[[2,7]] => [2] => [1,0,1,0] => 1010 => 1
[[3,7]] => [2] => [1,0,1,0] => 1010 => 1
[[4,7]] => [2] => [1,0,1,0] => 1010 => 1
[[5,7]] => [2] => [1,0,1,0] => 1010 => 1
[[6,7]] => [2] => [1,0,1,0] => 1010 => 1
[[7,7]] => [2] => [1,0,1,0] => 1010 => 1
[[1],[7]] => [1,1] => [1,1,0,0] => 1100 => 1
[[2],[7]] => [1,1] => [1,1,0,0] => 1100 => 1
[[3],[7]] => [1,1] => [1,1,0,0] => 1100 => 1
[[4],[7]] => [1,1] => [1,1,0,0] => 1100 => 1
[[5],[7]] => [1,1] => [1,1,0,0] => 1100 => 1
[[6],[7]] => [1,1] => [1,1,0,0] => 1100 => 1
[[1,1,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,2,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,3,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,4,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,5,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,6,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,2,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,3,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,4,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,5,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,6,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,3,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,4,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,5,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,6,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,4,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,5,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,6,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[5,5,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[5,6,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[6,6,6]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,1],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,2],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,6],[2]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,3],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,6],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,4],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,6],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,5],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,6],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,6],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,2],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,3],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,6],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,4],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,6],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,5],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,6],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,6],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,3],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,4],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,6],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,5],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,6],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,6],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,4],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,5],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,6],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,6],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[5,5],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[5,6],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1],[2],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[3],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[4],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[5],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[3],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[4],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[5],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[3],[4],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[3],[5],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[4],[5],[6]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1,1],[2,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[3,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[2,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[3,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[2,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[2,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[3,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[3,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[3,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[3,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,4],[3,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,4],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,4],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,3],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,3],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,4],[4,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,4],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[4,4],[5,5]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,8]] => [2] => [1,0,1,0] => 1010 => 1
[[2,8]] => [2] => [1,0,1,0] => 1010 => 1
[[3,8]] => [2] => [1,0,1,0] => 1010 => 1
[[4,8]] => [2] => [1,0,1,0] => 1010 => 1
[[5,8]] => [2] => [1,0,1,0] => 1010 => 1
[[6,8]] => [2] => [1,0,1,0] => 1010 => 1
[[7,8]] => [2] => [1,0,1,0] => 1010 => 1
[[8,8]] => [2] => [1,0,1,0] => 1010 => 1
[[1],[8]] => [1,1] => [1,1,0,0] => 1100 => 1
[[2],[8]] => [1,1] => [1,1,0,0] => 1100 => 1
[[3],[8]] => [1,1] => [1,1,0,0] => 1100 => 1
[[4],[8]] => [1,1] => [1,1,0,0] => 1100 => 1
[[5],[8]] => [1,1] => [1,1,0,0] => 1100 => 1
[[6],[8]] => [1,1] => [1,1,0,0] => 1100 => 1
[[7],[8]] => [1,1] => [1,1,0,0] => 1100 => 1
[[1,1,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,2,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,3,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,4,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,5,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,6,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,7,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,2,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,3,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,4,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,5,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,6,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[2,7,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,3,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,4,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,5,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,6,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[3,7,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,4,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,5,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,6,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4,7,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[5,5,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[5,6,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[5,7,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[6,6,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[6,7,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[7,7,7]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[1,1],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,2],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,7],[2]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,3],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,7],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,4],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,7],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,5],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,7],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,6],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,7],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1,7],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,2],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,3],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,7],[3]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,4],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,7],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,5],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,7],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,6],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,7],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[2,7],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,3],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,4],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,7],[4]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,5],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,7],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,6],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,7],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[3,7],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,4],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,5],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,7],[5]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,6],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,7],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[4,7],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[5,5],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[5,6],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[5,7],[6]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[5,7],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[6,6],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[6,7],[7]] => [2,1] => [1,0,1,1,0,0] => 101100 => 1
[[1],[2],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[3],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[4],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[5],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[3],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[4],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[5],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[2],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[3],[4],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[3],[5],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[3],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[4],[5],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[4],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[5],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => 110100 => 2
[[1,1],[2,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,1],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[2,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[2,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[2,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,5],[2,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,2],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,5],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,3],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,5],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,4],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,5],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1,5],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,2],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,4],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,5],[3,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,3],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,4],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,4],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,5],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,4],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,5],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[2,5],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,3],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,3],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,3],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,4],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,4],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,5],[4,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,4],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,5],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[3,5],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[4,4],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[4,4],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[4,5],[5,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[4,5],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[5,5],[6,6]] => [2,2] => [1,1,1,0,0,0] => 111000 => 1
[[1]] => [1] => [1,0] => 10 => 1
[[2]] => [1] => [1,0] => 10 => 1
[[1,1]] => [2] => [1,0,1,0] => 1010 => 1
[[3]] => [1] => [1,0] => 10 => 1
[[1,1,1]] => [3] => [1,0,1,0,1,0] => 101010 => 1
[[4]] => [1] => [1,0] => 10 => 1
[[5]] => [1] => [1,0] => 10 => 1
[[6]] => [1] => [1,0] => 10 => 1
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 minimal chains with small intervals between a binary word and the top element.
A valley in a binary word is a subsequence 01, or a trailing 0. A peak is a subsequence 10 or a trailing 1. Let P be the lattice on binary words of length n, where the covering elements of a word are obtained by replacing a valley with a peak. An interval [w1,w2] in P is small if w2 is obtained from w1 by replacing some valleys with peaks.
This statistic counts the number of chains w=w1<<wd=11 to the top element of minimal length.
For example, there are two such chains for the word 0110:
0110<1011<1101<1110<1111
and
0110<1010<1101<1110<1111.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
shape
Description
Return the shape of a tableau.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.