Identifier
Values
[1,1] => [1] => [1,0] => [1,0] => 1
[2,1] => [1] => [1,0] => [1,0] => 1
[1,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[3,1] => [1] => [1,0] => [1,0] => 1
[2,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[2,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[4,1] => [1] => [1,0] => [1,0] => 1
[3,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[3,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[2,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[5,1] => [1] => [1,0] => [1,0] => 1
[4,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[4,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[3,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[3,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[2,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[6,1] => [1] => [1,0] => [1,0] => 1
[5,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[5,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[4,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[4,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[3,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[7,1] => [1] => [1,0] => [1,0] => 1
[6,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[6,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[5,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[5,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[4,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[4,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[8,1] => [1] => [1,0] => [1,0] => 1
[7,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[7,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[6,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[6,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[5,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[5,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[9,1] => [1] => [1,0] => [1,0] => 1
[8,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[8,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[7,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[7,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[7,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[6,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[6,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
>>> Load all 319 entries. <<<
[3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[2,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[10,1] => [1] => [1,0] => [1,0] => 1
[9,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[9,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[8,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[8,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[8,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[7,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[7,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[7,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[7,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[6,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[6,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 4
[3,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[11,1] => [1] => [1,0] => [1,0] => 1
[10,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[10,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[9,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[9,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[9,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[8,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[8,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[8,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[8,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[7,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[7,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[7,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[7,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[7,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[6,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[6,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 4
[4,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[12,1] => [1] => [1,0] => [1,0] => 1
[11,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[11,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[10,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[10,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[10,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[9,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[9,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[9,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[9,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[8,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[8,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[8,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[8,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[8,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[7,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[7,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[7,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[7,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[7,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[6,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[6,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[6,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 4
[5,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[4,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[13,1] => [1] => [1,0] => [1,0] => 1
[12,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[12,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[11,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[11,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[11,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[10,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[10,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[10,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[10,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[9,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[9,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[9,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[9,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[9,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[8,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[8,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[8,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[8,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[8,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[7,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[7,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[7,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[7,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[6,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 4
[6,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[5,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[14,1] => [1] => [1,0] => [1,0] => 1
[13,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[13,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[12,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[12,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[12,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[11,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[11,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[11,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[11,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[10,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[10,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[10,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[10,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[10,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[9,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[9,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[9,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[9,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[9,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[8,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[8,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[8,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[8,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[7,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[7,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 4
[7,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[6,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[15,1] => [1] => [1,0] => [1,0] => 1
[14,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[14,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[13,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[13,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[13,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[12,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[12,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[12,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[12,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[11,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[11,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[11,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[11,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[11,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[10,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[10,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[10,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[10,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[10,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[9,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[9,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[9,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[9,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[8,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[8,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 4
[8,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[7,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[16,1] => [1] => [1,0] => [1,0] => 1
[15,2] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[15,1,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[14,3] => [3] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[14,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[14,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 2
[13,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[13,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[13,2,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[13,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[12,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[12,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[12,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[12,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[12,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[11,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[11,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 3
[11,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[11,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[11,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[10,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[10,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[10,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[10,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[9,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[9,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 4
[9,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[8,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[10,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
search for individual values
searching the database for the individual values of this statistic
Description
The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule).
Map
first row removal
Description
Removes the first entry of an integer partition
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.
Map
Elizalde-Deutsch bijection
Description
The Elizalde-Deutsch bijection on Dyck paths.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.