Identifier
-
Mp00311:
Plane partitions
—to partition⟶
Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St000288: Binary words ⟶ ℤ
Values
[[1]] => [1] => [1] => 1 => 1
[[1],[1]] => [1,1] => [2] => 0 => 0
[[2]] => [2] => [1,1] => 11 => 2
[[1,1]] => [2] => [1,1] => 11 => 2
[[1],[1],[1]] => [1,1,1] => [3] => 1 => 1
[[2],[1]] => [2,1] => [2,1] => 01 => 1
[[1,1],[1]] => [2,1] => [2,1] => 01 => 1
[[3]] => [3] => [1,1,1] => 111 => 3
[[2,1]] => [3] => [1,1,1] => 111 => 3
[[1,1,1]] => [3] => [1,1,1] => 111 => 3
[[1],[1],[1],[1]] => [1,1,1,1] => [4] => 0 => 0
[[2],[1],[1]] => [2,1,1] => [3,1] => 11 => 2
[[2],[2]] => [2,2] => [2,2] => 00 => 0
[[1,1],[1],[1]] => [2,1,1] => [3,1] => 11 => 2
[[1,1],[1,1]] => [2,2] => [2,2] => 00 => 0
[[3],[1]] => [3,1] => [2,1,1] => 011 => 2
[[2,1],[1]] => [3,1] => [2,1,1] => 011 => 2
[[1,1,1],[1]] => [3,1] => [2,1,1] => 011 => 2
[[4]] => [4] => [1,1,1,1] => 1111 => 4
[[3,1]] => [4] => [1,1,1,1] => 1111 => 4
[[2,2]] => [4] => [1,1,1,1] => 1111 => 4
[[2,1,1]] => [4] => [1,1,1,1] => 1111 => 4
[[1,1,1,1]] => [4] => [1,1,1,1] => 1111 => 4
[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => [5] => 1 => 1
[[2],[1],[1],[1]] => [2,1,1,1] => [4,1] => 01 => 1
[[2],[2],[1]] => [2,2,1] => [3,2] => 10 => 1
[[1,1],[1],[1],[1]] => [2,1,1,1] => [4,1] => 01 => 1
[[1,1],[1,1],[1]] => [2,2,1] => [3,2] => 10 => 1
[[3],[1],[1]] => [3,1,1] => [3,1,1] => 111 => 3
[[3],[2]] => [3,2] => [2,2,1] => 001 => 1
[[2,1],[1],[1]] => [3,1,1] => [3,1,1] => 111 => 3
[[2,1],[2]] => [3,2] => [2,2,1] => 001 => 1
[[2,1],[1,1]] => [3,2] => [2,2,1] => 001 => 1
[[1,1,1],[1],[1]] => [3,1,1] => [3,1,1] => 111 => 3
[[1,1,1],[1,1]] => [3,2] => [2,2,1] => 001 => 1
[[4],[1]] => [4,1] => [2,1,1,1] => 0111 => 3
[[3,1],[1]] => [4,1] => [2,1,1,1] => 0111 => 3
[[2,2],[1]] => [4,1] => [2,1,1,1] => 0111 => 3
[[2,1,1],[1]] => [4,1] => [2,1,1,1] => 0111 => 3
[[1,1,1,1],[1]] => [4,1] => [2,1,1,1] => 0111 => 3
[[5]] => [5] => [1,1,1,1,1] => 11111 => 5
[[4,1]] => [5] => [1,1,1,1,1] => 11111 => 5
[[3,2]] => [5] => [1,1,1,1,1] => 11111 => 5
[[3,1,1]] => [5] => [1,1,1,1,1] => 11111 => 5
[[2,2,1]] => [5] => [1,1,1,1,1] => 11111 => 5
[[2,1,1,1]] => [5] => [1,1,1,1,1] => 11111 => 5
[[1,1,1,1,1]] => [5] => [1,1,1,1,1] => 11111 => 5
[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => [6] => 0 => 0
[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => [5,1] => 11 => 2
[[2],[2],[1],[1]] => [2,2,1,1] => [4,2] => 00 => 0
[[2],[2],[2]] => [2,2,2] => [3,3] => 11 => 2
[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => [5,1] => 11 => 2
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => [4,2] => 00 => 0
[[1,1],[1,1],[1,1]] => [2,2,2] => [3,3] => 11 => 2
[[3],[1],[1],[1]] => [3,1,1,1] => [4,1,1] => 011 => 2
[[3],[2],[1]] => [3,2,1] => [3,2,1] => 101 => 2
[[3],[3]] => [3,3] => [2,2,2] => 000 => 0
[[2,1],[1],[1],[1]] => [3,1,1,1] => [4,1,1] => 011 => 2
[[2,1],[2],[1]] => [3,2,1] => [3,2,1] => 101 => 2
[[2,1],[1,1],[1]] => [3,2,1] => [3,2,1] => 101 => 2
[[2,1],[2,1]] => [3,3] => [2,2,2] => 000 => 0
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => [4,1,1] => 011 => 2
[[1,1,1],[1,1],[1]] => [3,2,1] => [3,2,1] => 101 => 2
[[1,1,1],[1,1,1]] => [3,3] => [2,2,2] => 000 => 0
[[4],[1],[1]] => [4,1,1] => [3,1,1,1] => 1111 => 4
[[4],[2]] => [4,2] => [2,2,1,1] => 0011 => 2
[[3,1],[1],[1]] => [4,1,1] => [3,1,1,1] => 1111 => 4
[[3,1],[2]] => [4,2] => [2,2,1,1] => 0011 => 2
[[3,1],[1,1]] => [4,2] => [2,2,1,1] => 0011 => 2
[[2,2],[1],[1]] => [4,1,1] => [3,1,1,1] => 1111 => 4
[[2,2],[2]] => [4,2] => [2,2,1,1] => 0011 => 2
[[2,2],[1,1]] => [4,2] => [2,2,1,1] => 0011 => 2
[[2,1,1],[1],[1]] => [4,1,1] => [3,1,1,1] => 1111 => 4
[[2,1,1],[2]] => [4,2] => [2,2,1,1] => 0011 => 2
[[2,1,1],[1,1]] => [4,2] => [2,2,1,1] => 0011 => 2
[[1,1,1,1],[1],[1]] => [4,1,1] => [3,1,1,1] => 1111 => 4
[[1,1,1,1],[1,1]] => [4,2] => [2,2,1,1] => 0011 => 2
[[5],[1]] => [5,1] => [2,1,1,1,1] => 01111 => 4
[[4,1],[1]] => [5,1] => [2,1,1,1,1] => 01111 => 4
[[3,2],[1]] => [5,1] => [2,1,1,1,1] => 01111 => 4
[[3,1,1],[1]] => [5,1] => [2,1,1,1,1] => 01111 => 4
[[2,2,1],[1]] => [5,1] => [2,1,1,1,1] => 01111 => 4
[[2,1,1,1],[1]] => [5,1] => [2,1,1,1,1] => 01111 => 4
[[1,1,1,1,1],[1]] => [5,1] => [2,1,1,1,1] => 01111 => 4
[[6]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[5,1]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[4,2]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[4,1,1]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[3,3]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[3,2,1]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[3,1,1,1]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[2,2,2]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[2,2,1,1]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[2,1,1,1,1]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[1,1,1,1,1,1]] => [6] => [1,1,1,1,1,1] => 111111 => 6
[[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1] => [7] => 1 => 1
[[2],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => [6,1] => 01 => 1
[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => [5,2] => 10 => 1
[[2],[2],[2],[1]] => [2,2,2,1] => [4,3] => 01 => 1
[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => [6,1] => 01 => 1
[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => [5,2] => 10 => 1
>>> Load all 1081 entries. <<<[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => [4,3] => 01 => 1
[[3],[1],[1],[1],[1]] => [3,1,1,1,1] => [5,1,1] => 111 => 3
[[3],[2],[1],[1]] => [3,2,1,1] => [4,2,1] => 001 => 1
[[3],[2],[2]] => [3,2,2] => [3,3,1] => 111 => 3
[[3],[3],[1]] => [3,3,1] => [3,2,2] => 100 => 1
[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [5,1,1] => 111 => 3
[[2,1],[2],[1],[1]] => [3,2,1,1] => [4,2,1] => 001 => 1
[[2,1],[2],[2]] => [3,2,2] => [3,3,1] => 111 => 3
[[2,1],[1,1],[1],[1]] => [3,2,1,1] => [4,2,1] => 001 => 1
[[2,1],[1,1],[1,1]] => [3,2,2] => [3,3,1] => 111 => 3
[[2,1],[2,1],[1]] => [3,3,1] => [3,2,2] => 100 => 1
[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [5,1,1] => 111 => 3
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => [4,2,1] => 001 => 1
[[1,1,1],[1,1],[1,1]] => [3,2,2] => [3,3,1] => 111 => 3
[[1,1,1],[1,1,1],[1]] => [3,3,1] => [3,2,2] => 100 => 1
[[4],[1],[1],[1]] => [4,1,1,1] => [4,1,1,1] => 0111 => 3
[[4],[2],[1]] => [4,2,1] => [3,2,1,1] => 1011 => 3
[[4],[3]] => [4,3] => [2,2,2,1] => 0001 => 1
[[3,1],[1],[1],[1]] => [4,1,1,1] => [4,1,1,1] => 0111 => 3
[[3,1],[2],[1]] => [4,2,1] => [3,2,1,1] => 1011 => 3
[[3,1],[1,1],[1]] => [4,2,1] => [3,2,1,1] => 1011 => 3
[[3,1],[3]] => [4,3] => [2,2,2,1] => 0001 => 1
[[3,1],[2,1]] => [4,3] => [2,2,2,1] => 0001 => 1
[[2,2],[1],[1],[1]] => [4,1,1,1] => [4,1,1,1] => 0111 => 3
[[2,2],[2],[1]] => [4,2,1] => [3,2,1,1] => 1011 => 3
[[2,2],[1,1],[1]] => [4,2,1] => [3,2,1,1] => 1011 => 3
[[2,2],[2,1]] => [4,3] => [2,2,2,1] => 0001 => 1
[[2,1,1],[1],[1],[1]] => [4,1,1,1] => [4,1,1,1] => 0111 => 3
[[2,1,1],[2],[1]] => [4,2,1] => [3,2,1,1] => 1011 => 3
[[2,1,1],[1,1],[1]] => [4,2,1] => [3,2,1,1] => 1011 => 3
[[2,1,1],[2,1]] => [4,3] => [2,2,2,1] => 0001 => 1
[[2,1,1],[1,1,1]] => [4,3] => [2,2,2,1] => 0001 => 1
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => [4,1,1,1] => 0111 => 3
[[1,1,1,1],[1,1],[1]] => [4,2,1] => [3,2,1,1] => 1011 => 3
[[1,1,1,1],[1,1,1]] => [4,3] => [2,2,2,1] => 0001 => 1
[[5],[1],[1]] => [5,1,1] => [3,1,1,1,1] => 11111 => 5
[[5],[2]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[4,1],[1],[1]] => [5,1,1] => [3,1,1,1,1] => 11111 => 5
[[4,1],[2]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[4,1],[1,1]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[3,2],[1],[1]] => [5,1,1] => [3,1,1,1,1] => 11111 => 5
[[3,2],[2]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[3,2],[1,1]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[3,1,1],[1],[1]] => [5,1,1] => [3,1,1,1,1] => 11111 => 5
[[3,1,1],[2]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[3,1,1],[1,1]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[2,2,1],[1],[1]] => [5,1,1] => [3,1,1,1,1] => 11111 => 5
[[2,2,1],[2]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[2,2,1],[1,1]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[2,1,1,1],[1],[1]] => [5,1,1] => [3,1,1,1,1] => 11111 => 5
[[2,1,1,1],[2]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[2,1,1,1],[1,1]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[1,1,1,1,1],[1],[1]] => [5,1,1] => [3,1,1,1,1] => 11111 => 5
[[1,1,1,1,1],[1,1]] => [5,2] => [2,2,1,1,1] => 00111 => 3
[[6],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[5,1],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[4,2],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[4,1,1],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[3,3],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[3,2,1],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[3,1,1,1],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[2,2,2],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[2,2,1,1],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[2,1,1,1,1],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[1,1,1,1,1,1],[1]] => [6,1] => [2,1,1,1,1,1] => 011111 => 5
[[7]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[6,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[5,2]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[5,1,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[4,3]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[4,2,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[4,1,1,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[3,3,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[3,2,2]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[3,2,1,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[3,1,1,1,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[2,2,2,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[2,2,1,1,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[2,1,1,1,1,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[1,1,1,1,1,1,1]] => [7] => [1,1,1,1,1,1,1] => 1111111 => 7
[[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1] => [8] => 0 => 0
[[2],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => [7,1] => 11 => 2
[[2],[2],[1],[1],[1],[1]] => [2,2,1,1,1,1] => [6,2] => 00 => 0
[[2],[2],[2],[1],[1]] => [2,2,2,1,1] => [5,3] => 11 => 2
[[2],[2],[2],[2]] => [2,2,2,2] => [4,4] => 00 => 0
[[1,1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => [7,1] => 11 => 2
[[1,1],[1,1],[1],[1],[1],[1]] => [2,2,1,1,1,1] => [6,2] => 00 => 0
[[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1] => [5,3] => 11 => 2
[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => [4,4] => 00 => 0
[[3],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [6,1,1] => 011 => 2
[[3],[2],[1],[1],[1]] => [3,2,1,1,1] => [5,2,1] => 101 => 2
[[3],[2],[2],[1]] => [3,2,2,1] => [4,3,1] => 011 => 2
[[3],[3],[1],[1]] => [3,3,1,1] => [4,2,2] => 000 => 0
[[3],[3],[2]] => [3,3,2] => [3,3,2] => 110 => 2
[[2,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [6,1,1] => 011 => 2
[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1] => [5,2,1] => 101 => 2
[[2,1],[2],[2],[1]] => [3,2,2,1] => [4,3,1] => 011 => 2
[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [5,2,1] => 101 => 2
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => [4,3,1] => 011 => 2
[[2,1],[2,1],[1],[1]] => [3,3,1,1] => [4,2,2] => 000 => 0
[[2,1],[2,1],[2]] => [3,3,2] => [3,3,2] => 110 => 2
[[2,1],[2,1],[1,1]] => [3,3,2] => [3,3,2] => 110 => 2
[[1,1,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [6,1,1] => 011 => 2
[[1,1,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [5,2,1] => 101 => 2
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => [4,3,1] => 011 => 2
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => [4,2,2] => 000 => 0
[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => [3,3,2] => 110 => 2
[[4],[1],[1],[1],[1]] => [4,1,1,1,1] => [5,1,1,1] => 1111 => 4
[[4],[2],[1],[1]] => [4,2,1,1] => [4,2,1,1] => 0011 => 2
[[4],[2],[2]] => [4,2,2] => [3,3,1,1] => 1111 => 4
[[4],[3],[1]] => [4,3,1] => [3,2,2,1] => 1001 => 2
[[4],[4]] => [4,4] => [2,2,2,2] => 0000 => 0
[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [5,1,1,1] => 1111 => 4
[[3,1],[2],[1],[1]] => [4,2,1,1] => [4,2,1,1] => 0011 => 2
[[3,1],[2],[2]] => [4,2,2] => [3,3,1,1] => 1111 => 4
[[3,1],[1,1],[1],[1]] => [4,2,1,1] => [4,2,1,1] => 0011 => 2
[[3,1],[1,1],[1,1]] => [4,2,2] => [3,3,1,1] => 1111 => 4
[[3,1],[3],[1]] => [4,3,1] => [3,2,2,1] => 1001 => 2
[[3,1],[2,1],[1]] => [4,3,1] => [3,2,2,1] => 1001 => 2
[[3,1],[3,1]] => [4,4] => [2,2,2,2] => 0000 => 0
[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1] => [5,1,1,1] => 1111 => 4
[[2,2],[2],[1],[1]] => [4,2,1,1] => [4,2,1,1] => 0011 => 2
[[2,2],[2],[2]] => [4,2,2] => [3,3,1,1] => 1111 => 4
[[2,2],[1,1],[1],[1]] => [4,2,1,1] => [4,2,1,1] => 0011 => 2
[[2,2],[1,1],[1,1]] => [4,2,2] => [3,3,1,1] => 1111 => 4
[[2,2],[2,1],[1]] => [4,3,1] => [3,2,2,1] => 1001 => 2
[[2,2],[2,2]] => [4,4] => [2,2,2,2] => 0000 => 0
[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [5,1,1,1] => 1111 => 4
[[2,1,1],[2],[1],[1]] => [4,2,1,1] => [4,2,1,1] => 0011 => 2
[[2,1,1],[2],[2]] => [4,2,2] => [3,3,1,1] => 1111 => 4
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => [4,2,1,1] => 0011 => 2
[[2,1,1],[1,1],[1,1]] => [4,2,2] => [3,3,1,1] => 1111 => 4
[[2,1,1],[2,1],[1]] => [4,3,1] => [3,2,2,1] => 1001 => 2
[[2,1,1],[1,1,1],[1]] => [4,3,1] => [3,2,2,1] => 1001 => 2
[[2,1,1],[2,1,1]] => [4,4] => [2,2,2,2] => 0000 => 0
[[1,1,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [5,1,1,1] => 1111 => 4
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => [4,2,1,1] => 0011 => 2
[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => [3,3,1,1] => 1111 => 4
[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => [3,2,2,1] => 1001 => 2
[[1,1,1,1],[1,1,1,1]] => [4,4] => [2,2,2,2] => 0000 => 0
[[5],[1],[1],[1]] => [5,1,1,1] => [4,1,1,1,1] => 01111 => 4
[[5],[2],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[5],[3]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[4,1],[1],[1],[1]] => [5,1,1,1] => [4,1,1,1,1] => 01111 => 4
[[4,1],[2],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[4,1],[1,1],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[4,1],[3]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[4,1],[2,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[3,2],[1],[1],[1]] => [5,1,1,1] => [4,1,1,1,1] => 01111 => 4
[[3,2],[2],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[3,2],[1,1],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[3,2],[3]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[3,2],[2,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[3,1,1],[1],[1],[1]] => [5,1,1,1] => [4,1,1,1,1] => 01111 => 4
[[3,1,1],[2],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[3,1,1],[1,1],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[3,1,1],[3]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[3,1,1],[2,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[3,1,1],[1,1,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[2,2,1],[1],[1],[1]] => [5,1,1,1] => [4,1,1,1,1] => 01111 => 4
[[2,2,1],[2],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[2,2,1],[1,1],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[2,2,1],[2,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[2,2,1],[1,1,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[2,1,1,1],[1],[1],[1]] => [5,1,1,1] => [4,1,1,1,1] => 01111 => 4
[[2,1,1,1],[2],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[2,1,1,1],[1,1],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[2,1,1,1],[2,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[2,1,1,1],[1,1,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1] => [4,1,1,1,1] => 01111 => 4
[[1,1,1,1,1],[1,1],[1]] => [5,2,1] => [3,2,1,1,1] => 10111 => 4
[[1,1,1,1,1],[1,1,1]] => [5,3] => [2,2,2,1,1] => 00011 => 2
[[6],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[6],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[5,1],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[5,1],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[5,1],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[4,2],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[4,2],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[4,2],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[4,1,1],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[4,1,1],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[4,1,1],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[3,3],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[3,3],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[3,3],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[3,2,1],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[3,2,1],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[3,2,1],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[3,1,1,1],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[3,1,1,1],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[3,1,1,1],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[2,2,2],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[2,2,2],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[2,2,2],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[2,2,1,1],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[2,2,1,1],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[2,2,1,1],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[2,1,1,1,1],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[2,1,1,1,1],[2]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[2,1,1,1,1],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[1,1,1,1,1,1],[1],[1]] => [6,1,1] => [3,1,1,1,1,1] => 111111 => 6
[[1,1,1,1,1,1],[1,1]] => [6,2] => [2,2,1,1,1,1] => 001111 => 4
[[7],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[6,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[5,2],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[5,1,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[4,3],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[4,2,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[4,1,1,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[3,3,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[3,2,2],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[3,2,1,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[3,1,1,1,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[2,2,2,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[2,2,1,1,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[2,1,1,1,1,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[1,1,1,1,1,1,1],[1]] => [7,1] => [2,1,1,1,1,1,1] => 0111111 => 6
[[8]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[7,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[6,2]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[6,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[5,3]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[5,2,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[5,1,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[4,4]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[4,3,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[4,2,2]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[4,2,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[4,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[3,3,2]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[3,3,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[3,2,2,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[3,2,1,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[3,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[2,2,2,2]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[2,2,2,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[2,2,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[2,1,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[1,1,1,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1] => [9] => 1 => 1
[[2],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => [8,1] => 01 => 1
[[2],[2],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => [7,2] => 10 => 1
[[2],[2],[2],[1],[1],[1]] => [2,2,2,1,1,1] => [6,3] => 01 => 1
[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => [5,4] => 10 => 1
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => [8,1] => 01 => 1
[[1,1],[1,1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => [7,2] => 10 => 1
[[1,1],[1,1],[1,1],[1],[1],[1]] => [2,2,2,1,1,1] => [6,3] => 01 => 1
[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => [5,4] => 10 => 1
[[3],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [7,1,1] => 111 => 3
[[3],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [6,2,1] => 001 => 1
[[3],[2],[2],[1],[1]] => [3,2,2,1,1] => [5,3,1] => 111 => 3
[[3],[2],[2],[2]] => [3,2,2,2] => [4,4,1] => 001 => 1
[[3],[3],[1],[1],[1]] => [3,3,1,1,1] => [5,2,2] => 100 => 1
[[3],[3],[2],[1]] => [3,3,2,1] => [4,3,2] => 010 => 1
[[3],[3],[3]] => [3,3,3] => [3,3,3] => 111 => 3
[[2,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [7,1,1] => 111 => 3
[[2,1],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [6,2,1] => 001 => 1
[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1] => [5,3,1] => 111 => 3
[[2,1],[2],[2],[2]] => [3,2,2,2] => [4,4,1] => 001 => 1
[[2,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [6,2,1] => 001 => 1
[[2,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => [5,3,1] => 111 => 3
[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [4,4,1] => 001 => 1
[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1] => [5,2,2] => 100 => 1
[[2,1],[2,1],[2],[1]] => [3,3,2,1] => [4,3,2] => 010 => 1
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => [4,3,2] => 010 => 1
[[2,1],[2,1],[2,1]] => [3,3,3] => [3,3,3] => 111 => 3
[[1,1,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [7,1,1] => 111 => 3
[[1,1,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [6,2,1] => 001 => 1
[[1,1,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => [5,3,1] => 111 => 3
[[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [4,4,1] => 001 => 1
[[1,1,1],[1,1,1],[1],[1],[1]] => [3,3,1,1,1] => [5,2,2] => 100 => 1
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => [4,3,2] => 010 => 1
[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => [3,3,3] => 111 => 3
[[4],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [6,1,1,1] => 0111 => 3
[[4],[2],[1],[1],[1]] => [4,2,1,1,1] => [5,2,1,1] => 1011 => 3
[[4],[2],[2],[1]] => [4,2,2,1] => [4,3,1,1] => 0111 => 3
[[4],[3],[1],[1]] => [4,3,1,1] => [4,2,2,1] => 0001 => 1
[[4],[3],[2]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[4],[4],[1]] => [4,4,1] => [3,2,2,2] => 1000 => 1
[[3,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [6,1,1,1] => 0111 => 3
[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [5,2,1,1] => 1011 => 3
[[3,1],[2],[2],[1]] => [4,2,2,1] => [4,3,1,1] => 0111 => 3
[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [5,2,1,1] => 1011 => 3
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => [4,3,1,1] => 0111 => 3
[[3,1],[3],[1],[1]] => [4,3,1,1] => [4,2,2,1] => 0001 => 1
[[3,1],[3],[2]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[3,1],[2,1],[1],[1]] => [4,3,1,1] => [4,2,2,1] => 0001 => 1
[[3,1],[2,1],[2]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[3,1],[2,1],[1,1]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[3,1],[3,1],[1]] => [4,4,1] => [3,2,2,2] => 1000 => 1
[[2,2],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [6,1,1,1] => 0111 => 3
[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1] => [5,2,1,1] => 1011 => 3
[[2,2],[2],[2],[1]] => [4,2,2,1] => [4,3,1,1] => 0111 => 3
[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [5,2,1,1] => 1011 => 3
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => [4,3,1,1] => 0111 => 3
[[2,2],[2,1],[1],[1]] => [4,3,1,1] => [4,2,2,1] => 0001 => 1
[[2,2],[2,1],[2]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[2,2],[2,1],[1,1]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[2,2],[2,2],[1]] => [4,4,1] => [3,2,2,2] => 1000 => 1
[[2,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [6,1,1,1] => 0111 => 3
[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [5,2,1,1] => 1011 => 3
[[2,1,1],[2],[2],[1]] => [4,2,2,1] => [4,3,1,1] => 0111 => 3
[[2,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [5,2,1,1] => 1011 => 3
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [4,3,1,1] => 0111 => 3
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => [4,2,2,1] => 0001 => 1
[[2,1,1],[2,1],[2]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[2,1,1],[2,1],[1,1]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [4,2,2,1] => 0001 => 1
[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[2,1,1],[2,1,1],[1]] => [4,4,1] => [3,2,2,2] => 1000 => 1
[[1,1,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [6,1,1,1] => 0111 => 3
[[1,1,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [5,2,1,1] => 1011 => 3
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [4,3,1,1] => 0111 => 3
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [4,2,2,1] => 0001 => 1
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => [3,3,2,1] => 1101 => 3
[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => [3,2,2,2] => 1000 => 1
[[5],[1],[1],[1],[1]] => [5,1,1,1,1] => [5,1,1,1,1] => 11111 => 5
[[5],[2],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[5],[2],[2]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[5],[3],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[5],[4]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [5,1,1,1,1] => 11111 => 5
[[4,1],[2],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[4,1],[2],[2]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[4,1],[1,1],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[4,1],[1,1],[1,1]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[4,1],[3],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[4,1],[2,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[4,1],[4]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[4,1],[3,1]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1] => [5,1,1,1,1] => 11111 => 5
[[3,2],[2],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[3,2],[2],[2]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[3,2],[1,1],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[3,2],[1,1],[1,1]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[3,2],[3],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[3,2],[2,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[3,2],[3,1]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[3,2],[2,2]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [5,1,1,1,1] => 11111 => 5
[[3,1,1],[2],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[3,1,1],[2],[2]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[3,1,1],[1,1],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[3,1,1],[1,1],[1,1]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[3,1,1],[3],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[3,1,1],[2,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[3,1,1],[1,1,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[3,1,1],[3,1]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[3,1,1],[2,1,1]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [5,1,1,1,1] => 11111 => 5
[[2,2,1],[2],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[2,2,1],[2],[2]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[2,2,1],[1,1],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[2,2,1],[1,1],[1,1]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[2,2,1],[2,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[2,2,1],[1,1,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[2,2,1],[2,2]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[2,2,1],[2,1,1]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[2,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [5,1,1,1,1] => 11111 => 5
[[2,1,1,1],[2],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[2,1,1,1],[2],[2]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[2,1,1,1],[1,1],[1,1]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[2,1,1,1],[2,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[2,1,1,1],[1,1,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[2,1,1,1],[2,1,1]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[2,1,1,1],[1,1,1,1]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[1,1,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [5,1,1,1,1] => 11111 => 5
[[1,1,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [4,2,1,1,1] => 00111 => 3
[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2] => [3,3,1,1,1] => 11111 => 5
[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1] => [3,2,2,1,1] => 10011 => 3
[[1,1,1,1,1],[1,1,1,1]] => [5,4] => [2,2,2,2,1] => 00001 => 1
[[6],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[6],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[6],[3]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[5,1],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[5,1],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[5,1],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[5,1],[3]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[5,1],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[4,2],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[4,2],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[4,2],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[4,2],[3]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[4,2],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[4,1,1],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[4,1,1],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[4,1,1],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[4,1,1],[3]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[4,1,1],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[4,1,1],[1,1,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[3,3],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[3,3],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[3,3],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[3,3],[3]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[3,3],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[3,2,1],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[3,2,1],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[3,2,1],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[3,2,1],[3]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[3,2,1],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[3,2,1],[1,1,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[3,1,1,1],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[3,1,1,1],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[3,1,1,1],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[3,1,1,1],[3]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[3,1,1,1],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[3,1,1,1],[1,1,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[2,2,2],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[2,2,2],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[2,2,2],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[2,2,2],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[2,2,2],[1,1,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[2,2,1,1],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[2,2,1,1],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[2,2,1,1],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[2,2,1,1],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[2,2,1,1],[1,1,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[2,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[2,1,1,1,1],[2],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[2,1,1,1,1],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[2,1,1,1,1],[2,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[2,1,1,1,1],[1,1,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[1,1,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => [4,1,1,1,1,1] => 011111 => 5
[[1,1,1,1,1,1],[1,1],[1]] => [6,2,1] => [3,2,1,1,1,1] => 101111 => 5
[[1,1,1,1,1,1],[1,1,1]] => [6,3] => [2,2,2,1,1,1] => 000111 => 3
[[7],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[7],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[6,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[6,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[6,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[5,2],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[5,2],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[5,2],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[5,1,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[5,1,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[5,1,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[4,3],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[4,3],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[4,3],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[4,2,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[4,2,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[4,2,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[4,1,1,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[4,1,1,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[4,1,1,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[3,3,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[3,3,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[3,3,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[3,2,2],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[3,2,2],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[3,2,2],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[3,2,1,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[3,2,1,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[3,2,1,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[3,1,1,1,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[3,1,1,1,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[3,1,1,1,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[2,2,2,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[2,2,2,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[2,2,2,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[2,2,1,1,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[2,2,1,1,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[2,2,1,1,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[2,1,1,1,1,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[2,1,1,1,1,1],[2]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[2,1,1,1,1,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[1,1,1,1,1,1,1],[1],[1]] => [7,1,1] => [3,1,1,1,1,1,1] => 1111111 => 7
[[1,1,1,1,1,1,1],[1,1]] => [7,2] => [2,2,1,1,1,1,1] => 0011111 => 5
[[8],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[7,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[6,2],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[6,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[5,3],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[5,2,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[5,1,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[4,4],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[4,3,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[4,2,2],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[4,2,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[4,1,1,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[3,3,2],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[3,3,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[3,2,2,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[3,2,1,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[3,1,1,1,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[2,2,2,2],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[2,2,2,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[2,2,1,1,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[2,1,1,1,1,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[1,1,1,1,1,1,1,1],[1]] => [8,1] => [2,1,1,1,1,1,1,1] => 01111111 => 7
[[9]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[8,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[7,2]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[7,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[6,3]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[6,2,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[6,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[5,4]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[5,3,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[5,2,2]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[5,2,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[5,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[4,4,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[4,3,2]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[4,3,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[4,2,2,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[4,2,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[4,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[3,3,3]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[3,3,2,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[3,3,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[3,2,2,2]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[3,2,2,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[3,2,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[3,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[2,2,2,2,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[2,2,2,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[2,2,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[2,1,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[1,1,1,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1,1] => [10] => 0 => 0
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => [9,1] => 11 => 2
[[2],[2],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => [8,2] => 00 => 0
[[2],[2],[2],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => [7,3] => 11 => 2
[[2],[2],[2],[2],[1],[1]] => [2,2,2,2,1,1] => [6,4] => 00 => 0
[[2],[2],[2],[2],[2]] => [2,2,2,2,2] => [5,5] => 11 => 2
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => [9,1] => 11 => 2
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => [8,2] => 00 => 0
[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => [7,3] => 11 => 2
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,2,1,1] => [6,4] => 00 => 0
[[1,1],[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2,2] => [5,5] => 11 => 2
[[3],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [8,1,1] => 011 => 2
[[3],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [7,2,1] => 101 => 2
[[3],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => [6,3,1] => 011 => 2
[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => [5,4,1] => 101 => 2
[[3],[3],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [6,2,2] => 000 => 0
[[3],[3],[2],[1],[1]] => [3,3,2,1,1] => [5,3,2] => 110 => 2
[[3],[3],[2],[2]] => [3,3,2,2] => [4,4,2] => 000 => 0
[[3],[3],[3],[1]] => [3,3,3,1] => [4,3,3] => 011 => 2
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [8,1,1] => 011 => 2
[[2,1],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [7,2,1] => 101 => 2
[[2,1],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => [6,3,1] => 011 => 2
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => [5,4,1] => 101 => 2
[[2,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [7,2,1] => 101 => 2
[[2,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => [6,3,1] => 011 => 2
[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [5,4,1] => 101 => 2
[[2,1],[2,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [6,2,2] => 000 => 0
[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1] => [5,3,2] => 110 => 2
[[2,1],[2,1],[2],[2]] => [3,3,2,2] => [4,4,2] => 000 => 0
[[2,1],[2,1],[1,1],[1],[1]] => [3,3,2,1,1] => [5,3,2] => 110 => 2
[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => [4,4,2] => 000 => 0
[[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => [4,3,3] => 011 => 2
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [8,1,1] => 011 => 2
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [7,2,1] => 101 => 2
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => [6,3,1] => 011 => 2
[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [5,4,1] => 101 => 2
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [6,2,2] => 000 => 0
[[1,1,1],[1,1,1],[1,1],[1],[1]] => [3,3,2,1,1] => [5,3,2] => 110 => 2
[[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2] => [4,4,2] => 000 => 0
[[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1] => [4,3,3] => 011 => 2
[[4],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [7,1,1,1] => 1111 => 4
[[4],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [6,2,1,1] => 0011 => 2
[[4],[2],[2],[1],[1]] => [4,2,2,1,1] => [5,3,1,1] => 1111 => 4
[[4],[2],[2],[2]] => [4,2,2,2] => [4,4,1,1] => 0011 => 2
[[4],[3],[1],[1],[1]] => [4,3,1,1,1] => [5,2,2,1] => 1001 => 2
[[4],[3],[2],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[4],[3],[3]] => [4,3,3] => [3,3,3,1] => 1111 => 4
[[4],[4],[1],[1]] => [4,4,1,1] => [4,2,2,2] => 0000 => 0
[[4],[4],[2]] => [4,4,2] => [3,3,2,2] => 1100 => 2
[[3,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [7,1,1,1] => 1111 => 4
[[3,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [6,2,1,1] => 0011 => 2
[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [5,3,1,1] => 1111 => 4
[[3,1],[2],[2],[2]] => [4,2,2,2] => [4,4,1,1] => 0011 => 2
[[3,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [6,2,1,1] => 0011 => 2
[[3,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [5,3,1,1] => 1111 => 4
[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [4,4,1,1] => 0011 => 2
[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1] => [5,2,2,1] => 1001 => 2
[[3,1],[3],[2],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[3,1],[3],[3]] => [4,3,3] => [3,3,3,1] => 1111 => 4
[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [5,2,2,1] => 1001 => 2
[[3,1],[2,1],[2],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[3,1],[2,1],[2,1]] => [4,3,3] => [3,3,3,1] => 1111 => 4
[[3,1],[3,1],[1],[1]] => [4,4,1,1] => [4,2,2,2] => 0000 => 0
[[3,1],[3,1],[2]] => [4,4,2] => [3,3,2,2] => 1100 => 2
[[3,1],[3,1],[1,1]] => [4,4,2] => [3,3,2,2] => 1100 => 2
[[2,2],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [7,1,1,1] => 1111 => 4
[[2,2],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [6,2,1,1] => 0011 => 2
[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1] => [5,3,1,1] => 1111 => 4
[[2,2],[2],[2],[2]] => [4,2,2,2] => [4,4,1,1] => 0011 => 2
[[2,2],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [6,2,1,1] => 0011 => 2
[[2,2],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [5,3,1,1] => 1111 => 4
[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2] => [4,4,1,1] => 0011 => 2
[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [5,2,2,1] => 1001 => 2
[[2,2],[2,1],[2],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[2,2],[2,1],[2,1]] => [4,3,3] => [3,3,3,1] => 1111 => 4
[[2,2],[2,2],[1],[1]] => [4,4,1,1] => [4,2,2,2] => 0000 => 0
[[2,2],[2,2],[2]] => [4,4,2] => [3,3,2,2] => 1100 => 2
[[2,2],[2,2],[1,1]] => [4,4,2] => [3,3,2,2] => 1100 => 2
[[2,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [7,1,1,1] => 1111 => 4
[[2,1,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [6,2,1,1] => 0011 => 2
[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [5,3,1,1] => 1111 => 4
[[2,1,1],[2],[2],[2]] => [4,2,2,2] => [4,4,1,1] => 0011 => 2
[[2,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [6,2,1,1] => 0011 => 2
[[2,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [5,3,1,1] => 1111 => 4
[[2,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [4,4,1,1] => 0011 => 2
[[2,1,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [5,2,2,1] => 1001 => 2
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[2,1,1],[2,1],[2,1]] => [4,3,3] => [3,3,3,1] => 1111 => 4
[[2,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => [5,2,2,1] => 1001 => 2
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [3,3,3,1] => 1111 => 4
[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1] => [4,2,2,2] => 0000 => 0
[[2,1,1],[2,1,1],[2]] => [4,4,2] => [3,3,2,2] => 1100 => 2
[[2,1,1],[2,1,1],[1,1]] => [4,4,2] => [3,3,2,2] => 1100 => 2
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [7,1,1,1] => 1111 => 4
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [6,2,1,1] => 0011 => 2
[[1,1,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [5,3,1,1] => 1111 => 4
[[1,1,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [4,4,1,1] => 0011 => 2
[[1,1,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => [5,2,2,1] => 1001 => 2
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [4,3,2,1] => 0101 => 2
[[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [3,3,3,1] => 1111 => 4
[[1,1,1,1],[1,1,1,1],[1],[1]] => [4,4,1,1] => [4,2,2,2] => 0000 => 0
[[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2] => [3,3,2,2] => 1100 => 2
[[5],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [6,1,1,1,1] => 01111 => 4
[[5],[2],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[5],[2],[2],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[5],[3],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[5],[3],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[5],[4],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[5],[5]] => [5,5] => [2,2,2,2,2] => 00000 => 0
[[4,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [6,1,1,1,1] => 01111 => 4
[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[4,1],[2],[2],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[4,1],[1,1],[1,1],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[4,1],[3],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[4,1],[3],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[4,1],[2,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[4,1],[2,1],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[4,1],[2,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[4,1],[4],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[4,1],[3,1],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[4,1],[4,1]] => [5,5] => [2,2,2,2,2] => 00000 => 0
[[3,2],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [6,1,1,1,1] => 01111 => 4
[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[3,2],[2],[2],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[3,2],[1,1],[1,1],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[3,2],[3],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[3,2],[3],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[3,2],[2,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[3,2],[2,1],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[3,2],[2,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[3,2],[3,1],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[3,2],[2,2],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[3,2],[3,2]] => [5,5] => [2,2,2,2,2] => 00000 => 0
[[3,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [6,1,1,1,1] => 01111 => 4
[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[3,1,1],[2],[2],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[3,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[3,1,1],[3],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[3,1,1],[3],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[3,1,1],[2,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[3,1,1],[2,1],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[3,1,1],[2,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[3,1,1],[1,1,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[3,1,1],[3,1],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[3,1,1],[2,1,1],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[3,1,1],[3,1,1]] => [5,5] => [2,2,2,2,2] => 00000 => 0
[[2,2,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [6,1,1,1,1] => 01111 => 4
[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[2,2,1],[2],[2],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[2,2,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[2,2,1],[2,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[2,2,1],[2,1],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[2,2,1],[2,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[2,2,1],[1,1,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[2,2,1],[2,2],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[2,2,1],[2,1,1],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[2,2,1],[2,2,1]] => [5,5] => [2,2,2,2,2] => 00000 => 0
[[2,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [6,1,1,1,1] => 01111 => 4
[[2,1,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[2,1,1,1],[2],[2],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[2,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[2,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[2,1,1,1],[2,1],[2]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[2,1,1,1],[2,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[2,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[2,1,1,1],[2,1,1],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[2,1,1,1],[2,1,1,1]] => [5,5] => [2,2,2,2,2] => 00000 => 0
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [6,1,1,1,1] => 01111 => 4
[[1,1,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [5,2,1,1,1] => 10111 => 4
[[1,1,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [4,3,1,1,1] => 01111 => 4
[[1,1,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [4,2,2,1,1] => 00011 => 2
[[1,1,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [3,3,2,1,1] => 11011 => 4
[[1,1,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [3,2,2,2,1] => 10001 => 2
[[1,1,1,1,1],[1,1,1,1,1]] => [5,5] => [2,2,2,2,2] => 00000 => 0
[[6],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[6],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[6],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[6],[3],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[6],[4]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[5,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[5,1],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[5,1],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[5,1],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[5,1],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[5,1],[3],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[5,1],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[5,1],[4]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[5,1],[3,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[4,2],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[4,2],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[4,2],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[4,2],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[4,2],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[4,2],[3],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[4,2],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[4,2],[4]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[4,2],[3,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[4,2],[2,2]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[4,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[4,1,1],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[4,1,1],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[4,1,1],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[4,1,1],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[4,1,1],[3],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[4,1,1],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[4,1,1],[1,1,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[4,1,1],[4]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[4,1,1],[3,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[4,1,1],[2,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[3,3],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[3,3],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[3,3],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[3,3],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[3,3],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[3,3],[3],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[3,3],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[3,3],[3,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[3,3],[2,2]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[3,2,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[3,2,1],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[3,2,1],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[3,2,1],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[3,2,1],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[3,2,1],[3],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[3,2,1],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[3,2,1],[1,1,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[3,2,1],[3,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[3,2,1],[2,2]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[3,2,1],[2,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[3,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[3,1,1,1],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[3,1,1,1],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[3,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[3,1,1,1],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[3,1,1,1],[3],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[3,1,1,1],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[3,1,1,1],[1,1,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[3,1,1,1],[3,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[3,1,1,1],[2,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[3,1,1,1],[1,1,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[2,2,2],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[2,2,2],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[2,2,2],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[2,2,2],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[2,2,2],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[2,2,2],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[2,2,2],[1,1,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[2,2,2],[2,2]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[2,2,2],[2,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[2,2,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[2,2,1,1],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[2,2,1,1],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[2,2,1,1],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[2,2,1,1],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[2,2,1,1],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[2,2,1,1],[1,1,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[2,2,1,1],[2,2]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[2,2,1,1],[2,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[2,2,1,1],[1,1,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[2,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[2,1,1,1,1],[2],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[2,1,1,1,1],[2],[2]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[2,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[2,1,1,1,1],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[2,1,1,1,1],[2,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[2,1,1,1,1],[1,1,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[2,1,1,1,1],[2,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[2,1,1,1,1],[1,1,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[1,1,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 111111 => 6
[[1,1,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [4,2,1,1,1,1] => 001111 => 4
[[1,1,1,1,1,1],[1,1],[1,1]] => [6,2,2] => [3,3,1,1,1,1] => 111111 => 6
[[1,1,1,1,1,1],[1,1,1],[1]] => [6,3,1] => [3,2,2,1,1,1] => 100111 => 4
[[1,1,1,1,1,1],[1,1,1,1]] => [6,4] => [2,2,2,2,1,1] => 000011 => 2
[[7],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[7],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[7],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[6,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[6,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[6,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[6,1],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[6,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[5,2],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[5,2],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[5,2],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[5,2],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[5,2],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[5,1,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[5,1,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[5,1,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[5,1,1],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[5,1,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[5,1,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[4,3],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[4,3],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[4,3],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[4,3],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[4,3],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[4,2,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[4,2,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[4,2,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[4,2,1],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[4,2,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[4,2,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[4,1,1,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[4,1,1,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[4,1,1,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[4,1,1,1],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[4,1,1,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[4,1,1,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,3,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[3,3,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[3,3,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[3,3,1],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,3,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,3,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,2,2],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[3,2,2],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[3,2,2],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[3,2,2],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,2,2],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,2,2],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,2,1,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[3,2,1,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[3,2,1,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[3,2,1,1],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,2,1,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,2,1,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[3,1,1,1,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[3,1,1,1,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[3,1,1,1,1],[3]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,1,1,1,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[3,1,1,1,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[2,2,2,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[2,2,2,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[2,2,2,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[2,2,2,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[2,2,2,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[2,2,1,1,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[2,2,1,1,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[2,2,1,1,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[2,2,1,1,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[2,2,1,1,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[2,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[2,1,1,1,1,1],[2],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[2,1,1,1,1,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[2,1,1,1,1,1],[2,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[2,1,1,1,1,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[1,1,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 0111111 => 6
[[1,1,1,1,1,1,1],[1,1],[1]] => [7,2,1] => [3,2,1,1,1,1,1] => 1011111 => 6
[[1,1,1,1,1,1,1],[1,1,1]] => [7,3] => [2,2,2,1,1,1,1] => 0001111 => 4
[[8],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[8],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[7,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[7,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[7,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[6,2],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[6,2],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[6,2],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[6,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[6,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[6,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[5,3],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[5,3],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[5,3],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[5,2,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[5,2,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[5,2,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[5,1,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[5,1,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[5,1,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,4],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[4,4],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,4],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,3,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[4,3,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,3,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,2,2],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[4,2,2],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,2,2],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,2,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[4,2,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,2,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,1,1,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[4,1,1,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[4,1,1,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,3,2],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[3,3,2],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,3,2],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,3,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[3,3,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,3,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,2,2,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[3,2,2,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,2,2,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,2,1,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[3,2,1,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,2,1,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,1,1,1,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[3,1,1,1,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[3,1,1,1,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[2,2,2,2],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[2,2,2,2],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[2,2,2,2],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[2,2,2,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[2,2,2,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[2,2,2,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[2,2,1,1,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[2,2,1,1,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[2,2,1,1,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[2,1,1,1,1,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[2,1,1,1,1,1,1],[2]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[2,1,1,1,1,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[1,1,1,1,1,1,1,1],[1],[1]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 11111111 => 8
[[1,1,1,1,1,1,1,1],[1,1]] => [8,2] => [2,2,1,1,1,1,1,1] => 00111111 => 6
[[9],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[8,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[7,2],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[7,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[6,3],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[6,2,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[6,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[5,4],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[5,3,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[5,2,2],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[5,2,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[5,1,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[4,4,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[4,3,2],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[4,3,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[4,2,2,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[4,2,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[4,1,1,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[3,3,3],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[3,3,2,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[3,3,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[3,2,2,2],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[3,2,2,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[3,2,1,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[3,1,1,1,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[2,2,2,2,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[2,2,2,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[2,2,1,1,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[2,1,1,1,1,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
[[1,1,1,1,1,1,1,1,1],[1]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 011111111 => 8
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,2 3,0,3 3,0,5,0,5 9,0,8,0,7 6,0,19,0,12,0,11 21,0,32,0,18,0,15 13,0,47,0,52,0,26,0,22 48,0,89,0,78,0,37,0,30
$F_{1} = q$
$F_{2} = 1 + 2\ q^{2}$
$F_{3} = 3\ q + 3\ q^{3}$
$F_{4} = 3 + 5\ q^{2} + 5\ q^{4}$
$F_{5} = 9\ q + 8\ q^{3} + 7\ q^{5}$
$F_{6} = 6 + 19\ q^{2} + 12\ q^{4} + 11\ q^{6}$
$F_{7} = 21\ q + 32\ q^{3} + 18\ q^{5} + 15\ q^{7}$
$F_{8} = 13 + 47\ q^{2} + 52\ q^{4} + 26\ q^{6} + 22\ q^{8}$
$F_{9} = 48\ q + 89\ q^{3} + 78\ q^{5} + 37\ q^{7} + 30\ q^{9}$
Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
This is also known as the Hamming weight of the word.
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to partition
Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
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conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
odd parts
Description
Return the binary word indicating which parts of the partition are odd.
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