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# rowPermutationTableaux(YoungTableau) -- the list of row permutations without repetitions in columns

## Synopsis

• Function: rowPermutationTableaux
• Usage:
rowPermutationTableaux(y)
• Inputs:
• y, an instance of the type YoungTableau, a tableau, generally the index tableau of a standard tableau
• Outputs:
• a list, the list of all row permutations of the tableau

## Description

This list of tableaux is used to calculate more efficiently higher Specht polynomials. If any of the columns has a repetition then the associated term in the higher Specht polynomial for this row permutation is zero. This is why such permutations are omitted.

 i1 : p = new Partition from {3,2} o1 = Partition{3, 2} o1 : Partition i2 : y = youngTableau(p, {0,2,1,3,4}) o2 = | 0 2 1 | | 3 4 | o2 : YoungTableau i3 : ind = indexTableau y o3 = | 0 1 0 | | 2 2 | o3 : YoungTableau i4 : rowPermutationTableaux ind o4 = {| 0 0 1 |, | 0 1 0 |, | 1 0 0 |} | 2 2 | | 2 2 | | 2 2 | o4 : List