Processing math: 100%

Identifier
Values
[1,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[2,2] => [2] => [[1,2]] => [1,2] => 1
[2,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[1,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[3,2] => [2] => [[1,2]] => [1,2] => 1
[3,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[2,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[2,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[4,2] => [2] => [[1,2]] => [1,2] => 1
[4,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[3,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[3,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[3,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[2,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[2,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[5,2] => [2] => [[1,2]] => [1,2] => 1
[5,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[4,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[4,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[4,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[3,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[3,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[3,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[6,2] => [2] => [[1,2]] => [1,2] => 1
[6,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[5,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[5,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[5,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[4,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[4,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[4,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[4,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[7,2] => [2] => [[1,2]] => [1,2] => 1
[7,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[6,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[6,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[6,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[5,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[5,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[5,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[5,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[8,2] => [2] => [[1,2]] => [1,2] => 1
[8,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[7,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[7,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[7,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[6,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[6,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[6,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[6,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[9,2] => [2] => [[1,2]] => [1,2] => 1
[9,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[8,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[8,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[8,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[7,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[7,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[7,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[7,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[10,2] => [2] => [[1,2]] => [1,2] => 1
[10,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[9,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[9,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[9,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[8,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[8,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[8,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[8,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[8,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[11,2] => [2] => [[1,2]] => [1,2] => 1
[11,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[10,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[10,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[10,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[9,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[9,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[9,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[9,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[9,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[12,2] => [2] => [[1,2]] => [1,2] => 1
[12,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[11,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[11,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[11,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[10,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[10,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[10,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[10,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[10,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[13,2] => [2] => [[1,2]] => [1,2] => 1
[13,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[12,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[12,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[12,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
>>> Load all 126 entries. <<<
[11,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[11,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[11,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[11,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[11,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[14,2] => [2] => [[1,2]] => [1,2] => 1
[14,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[13,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[13,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[13,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[12,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[12,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[12,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[12,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[12,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[15,2] => [2] => [[1,2]] => [1,2] => 1
[15,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[14,3] => [3] => [[1,2,3]] => [1,2,3] => 3
[14,2,1] => [2,1] => [[1,3],[2]] => [2,1,3] => 2
[14,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[13,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 6
[13,3,1] => [3,1] => [[1,3,4],[2]] => [2,1,3,4] => 5
[13,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[13,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => 3
[13,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
search for individual values
searching the database for the individual values of this statistic
Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau T labeled down (in English convention) each column to the shape of a partition.