rowStabilizer(YoungTableau) -- the row stabilizer of the tableau

Synopsis

Function: rowStabilizer
Usage:

rowStabilizer(y)
Inputs:
- y, an instance of the type YoungTableau,
Outputs:
- a list, a dubly nested list with the permutations in the row stabilizer

Description

The row stabilizer of a tableau is the group of the permutations that fixes the rows of the tableau. In terms of tabloids it is the stabilizer of a tabloid under the action of the group of permutations S_n. This group is used in the calculation of polytabloids and Specht polynomials.

i1 : p = new Partition from {2,2,1}

o1 = Partition{2, 2, 1}

o1 : Partition

i2 : y = youngTableau(p,{0,3,1,4,2})

o2 = | 0 3 |
     | 1 4 |
     | 2 |

o2 : YoungTableau

i3 : rowStabilizer y

o3 = {{0, 1, 2, 3, 4}, {0, 4, 2, 3, 1}, {3, 1, 2, 0, 4}, {3, 4, 2, 0, 1}}

o3 : List

Ways to use this method: