sortColumnsTableau(SpechtModuleElement) -- a method for sorting the columns of the tableaux in a SpechtModuleElement

Synopsis

Function: sortColumnsTableau
Usage:

sortColumnsTableau(ele)
Inputs:
- ele, an instance of the type SpechtModuleElement,
Outputs:

Description

This method sorts the columns of every tableaux that appears as a term of the SpechtModuleElement. The corresponding sign of the sort is multiplied to the coefficient of the respective term. The method returns null but changes the SpechtModuleElement that was input as a parameter.

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

o1 = Partition{2, 2, 1}

o1 : Partition

i2 : y1 = youngTableau(p,{0,1,4,3,2})

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

o2 : YoungTableau

i3 : y2 = youngTableau(p,{0,3,4,1,2})

o3 = | 0 3 |
     | 4 1 |
     | 2 |

o3 : YoungTableau

i4 : ele = spechtModuleElement(y1)-spechtModuleElement(y2)

o4 = | 0 1 | - | 0 3 |
     | 4 3 |   | 4 1 |
     | 2 |     | 2 |

o4 : SpechtModuleElement

i5 : sortColumnsTableau ele

i6 : ele

o6 = -2 | 0 1 |
        | 2 3 |
        | 4 |

o6 : SpechtModuleElement

Ways to use this method: