Identifier
Values
[1] => [[1]] => [[1]] => 0
[2] => [[1,2]] => [[1],[2]] => 0
[1,1] => [[1],[2]] => [[1,2]] => 1
[3] => [[1,2,3]] => [[1],[2],[3]] => 0
[2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 0
[3,1] => [[1,2,3],[4]] => [[1,4],[2],[3]] => 1
[2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[2,1,1] => [[1,2],[3],[4]] => [[1,3,4],[2]] => 3
[1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 6
[5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 0
[4,1] => [[1,2,3,4],[5]] => [[1,5],[2],[3],[4]] => 1
[3,2] => [[1,2,3],[4,5]] => [[1,4],[2,5],[3]] => 2
[3,1,1] => [[1,2,3],[4],[5]] => [[1,4,5],[2],[3]] => 3
[2,2,1] => [[1,2],[3,4],[5]] => [[1,3,5],[2,4]] => 4
[2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,3,4,5],[2]] => 6
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 10
[6] => [[1,2,3,4,5,6]] => [[1],[2],[3],[4],[5],[6]] => 0
[5,1] => [[1,2,3,4,5],[6]] => [[1,6],[2],[3],[4],[5]] => 1
[4,2] => [[1,2,3,4],[5,6]] => [[1,5],[2,6],[3],[4]] => 2
[4,1,1] => [[1,2,3,4],[5],[6]] => [[1,5,6],[2],[3],[4]] => 3
[3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 3
[3,2,1] => [[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => 4
[3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,4,5,6],[2],[3]] => 6
[2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 6
[2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => 7
[2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,3,4,5,6],[2]] => 10
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 15
[7] => [[1,2,3,4,5,6,7]] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[6,1] => [[1,2,3,4,5,6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 1
[5,2] => [[1,2,3,4,5],[6,7]] => [[1,6],[2,7],[3],[4],[5]] => 2
[5,1,1] => [[1,2,3,4,5],[6],[7]] => [[1,6,7],[2],[3],[4],[5]] => 3
[4,3] => [[1,2,3,4],[5,6,7]] => [[1,5],[2,6],[3,7],[4]] => 3
[4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => 4
[4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]] => 6
[3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,4,7],[2,5],[3,6]] => 5
[3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,4,6],[2,5,7],[3]] => 6
[3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 7
[3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => 10
[2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6]] => 9
[2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 11
[2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => 15
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 21
[8] => [[1,2,3,4,5,6,7,8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[7,1] => [[1,2,3,4,5,6,7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[6,2] => [[1,2,3,4,5,6],[7,8]] => [[1,7],[2,8],[3],[4],[5],[6]] => 2
[6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[5,3] => [[1,2,3,4,5],[6,7,8]] => [[1,6],[2,7],[3,8],[4],[5]] => 3
[5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => 4
[5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 4
[4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => 5
[4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,5,7],[2,6,8],[3],[4]] => 6
[4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 7
[4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => 10
[3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,4,7],[2,5,8],[3,6]] => 7
[3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,4,7,8],[2,5],[3,6]] => 8
[3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 9
[3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 11
[3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => 15
[2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 12
[2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 13
[2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 16
[2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => 21
[1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,3,4,5,6,7,8]] => 28
[9] => [[1,2,3,4,5,6,7,8,9]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 0
[8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 1
[7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 2
[7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 3
[6,3] => [[1,2,3,4,5,6],[7,8,9]] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 3
[6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 4
[6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 6
[5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[1,6],[2,7],[3,8],[4,9],[5]] => 4
[5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,6,9],[2,7],[3,8],[4],[5]] => 5
[5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,6,8],[2,7,9],[3],[4],[5]] => 6
[5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 7
[5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,6,7,8,9],[2],[3],[4],[5]] => 10
[4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [[1,5,9],[2,6],[3,7],[4,8]] => 6
[4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,5,8],[2,6,9],[3,7],[4]] => 7
[4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 8
[4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 9
[4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 11
[4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]] => 15
[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [[1,4,7],[2,5,8],[3,6,9]] => 9
[3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 10
[3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 12
[3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,4,6,8],[2,5,7,9],[3]] => 12
[3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 13
[3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 16
[3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 21
[2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3,5,7,9],[2,4,6,8]] => 16
[2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 18
[2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 22
[2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 28
[1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 36
[10] => [[1,2,3,4,5,6,7,8,9,10]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 0
[9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 2
[8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 3
[7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 3
>>> Load all 142 entries. <<<
[7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 4
[7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 6
[6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 4
[6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 5
[6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [[1,7,9],[2,8,10],[3],[4],[5],[6]] => 6
[6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 7
[6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 10
[5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 5
[5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 6
[5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 7
[5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 8
[5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 9
[5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 11
[5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 15
[4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [[1,5,9],[2,6,10],[3,7],[4,8]] => 8
[4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 9
[4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 9
[4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 10
[4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 12
[4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 12
[4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 13
[4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 16
[4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 21
[3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [[1,4,7,10],[2,5,8],[3,6,9]] => 12
[3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,4,7,9],[2,5,8,10],[3,6]] => 13
[3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 14
[3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 17
[3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 16
[3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 18
[3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 22
[3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 28
[2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [[1,3,5,7,9],[2,4,6,8,10]] => 20
[2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 21
[2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 24
[2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 29
[2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 36
[1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 45
[6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 6
[2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 30
[1,1,1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 66
[] => [] => [] => 0
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Description
The charge of a standard tableau.
Map
conjugate
Description
Sends a standard tableau to its conjugate tableau.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.