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

Ways to use this method: