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

## Synopsis

• Function: rowStabilizer
• Usage:
rowStabilizer(y)
• Inputs:
• 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