Processing math: 100%

Identifier
Values
[2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[3,1,1] => [[3,3,3],[2,2]] => [2,2] => [2] => 1
[1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => [2] => 1
[2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => [1,1] => 2
[2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => [2,1] => 1
[3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => [2,2] => 3
[3,1,2] => [[4,3,3],[2,2]] => [2,2] => [2] => 1
[3,2,1] => [[4,4,3],[3,2]] => [3,2] => [2] => 1
[4,1,1] => [[4,4,4],[3,3]] => [3,3] => [3] => 2
[1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => [2] => 1
[1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => [2,1] => 1
[1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => [2] => 1
[1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => [2] => 1
[1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => [3] => 2
[2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,1,1] => 5
[2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,1,1] => 3
[2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [2,1,1] => 2
[2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => [1,1] => 2
[2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => [1,1] => 2
[2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [2,2,1] => 4
[2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => [2,1] => 1
[2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => [2,1] => 1
[2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => [3,1] => 2
[3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => [2,2,2] => 5
[3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => [2,2] => 3
[3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => [2,2] => 3
[3,1,3] => [[5,3,3],[2,2]] => [2,2] => [2] => 1
[3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => [3,2] => 3
[3,2,2] => [[5,4,3],[3,2]] => [3,2] => [2] => 1
[3,3,1] => [[5,5,3],[4,2]] => [4,2] => [2] => 1
[4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => [3,3] => 6
[4,1,2] => [[5,4,4],[3,3]] => [3,3] => [3] => 2
[4,2,1] => [[5,5,4],[4,3]] => [4,3] => [3] => 2
[5,1,1] => [[5,5,5],[4,4]] => [4,4] => [4] => 2
[1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => [2,1] => 1
[1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => [2] => 1
[1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => [2] => 1
[1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,1,1] => 5
[1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,1,1] => 3
[1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [2,1,1] => 2
[1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => [1,1] => 2
[1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [2,2,1] => 4
[1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => [2,1] => 1
[1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => [2,1] => 1
[1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => [3,1] => 2
[1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => [2,2] => 3
[1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => [2] => 1
[1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => [3,2] => 3
[1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => [2] => 1
[1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => [2] => 1
[1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => [3,3] => 6
[1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => [3] => 2
[1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => [3] => 2
[2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [1,1,1,1,1] => 7
[2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,1,1] => 5
[2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => [1,1,1,1] => 5
[2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => [2,1,1,1] => 3
[2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,1,1] => 3
[2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => [1,1,1] => 3
[2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => [2,2,1,1] => 8
[2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [2,1,1] => 2
[2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => [2,1,1] => 2
[2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => [1,1] => 2
[2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => [3,1,1] => 4
[2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => [1,1] => 2
[2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => [2,2,2,1] => 5
[2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [2,2,1] => 4
[2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => [2,2,1] => 4
[2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => [2,1] => 1
[2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => [3,2,1] => 3
[2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => [2,1] => 1
[2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => [2,1] => 1
[2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => [3,3,1] => 5
[2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => [3,1] => 2
[2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => [3,1] => 2
[2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => [4,1] => 2
[3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => [2,2,2,2] => 10
[3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => [2,2,2] => 5
[3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => [2,2] => 3
[3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => [3,2,2] => 7
[3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => [2,2] => 3
[3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => [2,2] => 3
[3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => [3,3,2] => 9
[3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => [3,2] => 3
>>> Load all 125 entries. <<<
[3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => [3,2] => 3
[3,2,3] => [[6,4,3],[3,2]] => [3,2] => [2] => 1
[3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => [4,2] => 4
[3,3,2] => [[6,5,3],[4,2]] => [4,2] => [2] => 1
[3,4,1] => [[6,6,3],[5,2]] => [5,2] => [2] => 1
[4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => [3,3,3] => 13
[4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => [3,3] => 6
[4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => [3,3] => 6
[4,1,3] => [[6,4,4],[3,3]] => [3,3] => [3] => 2
[4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => [4,3] => 6
[4,2,2] => [[6,5,4],[4,3]] => [4,3] => [3] => 2
[4,3,1] => [[6,6,4],[5,3]] => [5,3] => [3] => 2
[5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => [4,4] => 8
[6,1,1] => [[6,6,6],[5,5]] => [5,5] => [5] => 3
[2,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 11
[3,1,1,1,1,1,1] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => [2,2,2,2,2] => 18
[4,1,1,1,1,1] => [[4,4,4,4,4,4],[3,3,3,3,3]] => [3,3,3,3,3] => [3,3,3,3] => 31
[5,1,1,1,1] => [[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4] => [4,4,4] => 20
[6,1,1,1] => [[6,6,6,6],[5,5,5]] => [5,5,5] => [5,5] => 12
[7,1,1] => [[7,7,7],[6,6]] => [6,6] => [6] => 3
[2,1,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 15
[3,1,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 31
[7,1,1,1] => [[7,7,7,7],[6,6,6]] => [6,6,6] => [6,6] => 15
[8,1,1] => [[8,8,8],[7,7]] => [7,7] => [7] => 4
search for individual values
searching the database for the individual values of this statistic
Description
The number of characters of the symmetric group whose value on the partition is positive.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition (a1,…,an), this is the ribbon shape whose ith row from the bottom has ai cells.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
inner shape
Description
The inner shape of a skew partition.