Identifier
Values
[1] => [[1]] => 0
[2] => [[1,2]] => 1
[1,1] => [[1],[2]] => 0
[3] => [[1,2,3]] => 3
[2,1] => [[1,2],[3]] => 2
[1,1,1] => [[1],[2],[3]] => 0
[4] => [[1,2,3,4]] => 6
[3,1] => [[1,2,3],[4]] => 5
[2,2] => [[1,2],[3,4]] => 4
[2,1,1] => [[1,2],[3],[4]] => 3
[1,1,1,1] => [[1],[2],[3],[4]] => 0
[5] => [[1,2,3,4,5]] => 10
[4,1] => [[1,2,3,4],[5]] => 9
[3,2] => [[1,2,3],[4,5]] => 8
[3,1,1] => [[1,2,3],[4],[5]] => 7
[2,2,1] => [[1,2],[3,4],[5]] => 6
[2,1,1,1] => [[1,2],[3],[4],[5]] => 4
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6] => [[1,2,3,4,5,6]] => 15
[5,1] => [[1,2,3,4,5],[6]] => 14
[4,2] => [[1,2,3,4],[5,6]] => 13
[4,1,1] => [[1,2,3,4],[5],[6]] => 12
[3,3] => [[1,2,3],[4,5,6]] => 12
[3,2,1] => [[1,2,3],[4,5],[6]] => 11
[3,1,1,1] => [[1,2,3],[4],[5],[6]] => 9
[2,2,2] => [[1,2],[3,4],[5,6]] => 9
[2,2,1,1] => [[1,2],[3,4],[5],[6]] => 8
[2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 5
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[7] => [[1,2,3,4,5,6,7]] => 21
[6,1] => [[1,2,3,4,5,6],[7]] => 20
[5,2] => [[1,2,3,4,5],[6,7]] => 19
[5,1,1] => [[1,2,3,4,5],[6],[7]] => 18
[4,3] => [[1,2,3,4],[5,6,7]] => 18
[4,2,1] => [[1,2,3,4],[5,6],[7]] => 17
[4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 15
[3,3,1] => [[1,2,3],[4,5,6],[7]] => 16
[3,2,2] => [[1,2,3],[4,5],[6,7]] => 15
[3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 14
[3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 11
[2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 12
[2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 10
[2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 6
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[8] => [[1,2,3,4,5,6,7,8]] => 28
[7,1] => [[1,2,3,4,5,6,7],[8]] => 27
[6,2] => [[1,2,3,4,5,6],[7,8]] => 26
[6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 25
[5,3] => [[1,2,3,4,5],[6,7,8]] => 25
[5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 24
[5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 22
[4,4] => [[1,2,3,4],[5,6,7,8]] => 24
[4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 23
[4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 22
[4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 21
[4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 18
[3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 21
[3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 20
[3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 19
[3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 17
[3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 13
[2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 16
[2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 15
[2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 12
[2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 7
[1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[9] => [[1,2,3,4,5,6,7,8,9]] => 36
[8,1] => [[1,2,3,4,5,6,7,8],[9]] => 35
[7,2] => [[1,2,3,4,5,6,7],[8,9]] => 34
[7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 33
[6,3] => [[1,2,3,4,5,6],[7,8,9]] => 33
[6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 32
[6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 30
[5,4] => [[1,2,3,4,5],[6,7,8,9]] => 32
[5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 31
[5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 30
[5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 29
[5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 26
[4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 30
[4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 29
[4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 28
[4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 27
[4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 25
[4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 21
[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 27
[3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 26
[3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 24
[3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 24
[3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 23
[3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 20
[3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 15
[2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 20
[2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 18
[2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 14
[2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 0
[10] => [[1,2,3,4,5,6,7,8,9,10]] => 45
[9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 44
[8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 43
[8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 42
[7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 42
>>> Load all 191 entries. <<<
[7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 41
[7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 39
[6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 41
[6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 40
[6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 39
[6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 38
[6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 35
[5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 40
[5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 39
[5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 38
[5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 37
[5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 36
[5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 34
[5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 30
[4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 37
[4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 36
[4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 36
[4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 35
[4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 33
[4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 33
[4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 32
[4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 29
[4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 24
[3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 33
[3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 32
[3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 31
[3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 28
[3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 29
[3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 27
[3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 23
[3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 17
[2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 25
[2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 24
[2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 21
[2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 16
[2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 0
[5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 47
[5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 46
[5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 46
[5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 45
[5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => 43
[5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 43
[5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 42
[4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 45
[4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 44
[4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 42
[4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 43
[4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => 42
[4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 41
[4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => 39
[3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 40
[3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 39
[3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 38
[12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 66
[6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 60
[6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 58
[5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 56
[5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 55
[5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 53
[5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 54
[5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 53
[5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 52
[5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 50
[4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 53
[4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 52
[4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 51
[4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 51
[4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 50
[4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 49
[3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 47
[3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 44
[2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 36
[5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 65
[5,4,2,2] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]] => 64
[5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 63
[5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 63
[5,3,3,1,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]] => 62
[5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 61
[4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 62
[4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 61
[4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => 60
[4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 59
[5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 75
[5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 74
[5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => 73
[5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 72
[4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 71
[5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 85
[] => [] => 0
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Description
The charge of a standard tableau.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.