TableauList -- the class of list of tableaux

Description

This type represents a list of tableaux of the same size. They are represented as a MutableHashTable. A matrix in this hash table stores the filling of every tableau in the list. This representation is particularly useful when only the filling of the tableau is needed.

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

o1 = Partition{2, 1}

o1 : Partition

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

o2 = | 0 1 |
     | 2 |

o2 : YoungTableau

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

o3 = | 0 2 |
     | 1 |

o3 : YoungTableau

i4 : y3 = youngTableau(p,{1,2,0})

o4 = | 1 2 |
     | 0 |

o4 : YoungTableau

i5 : t = tableauList p

o5 = {}

o5 : TableauList

i6 : addTableau(t, y1)

o6 = {| 0 1 |}
      | 2 |

o6 : TableauList

i7 : addTableau(t, y2)

o7 = {| 0 1 |, | 0 2 |}
      | 2 |    | 1 |

o7 : TableauList

i8 : addTableau(t, y3)

o8 = {| 0 1 |, | 0 2 |, | 1 2 |}
      | 2 |    | 1 |    | 0 |

o8 : TableauList

i9 : peek t

o9 = TableauList{length => 3                 }
                 matrix => | 0 1 2 |
                           | 0 2 1 |
                           | 1 2 0 |
                 partition => Partition{2, 1}

Functions and methods returning an object of class TableauList :

semistandardTableaux -- see semistandardTableaux(Partition,ZZ) -- the list of semistandard tableaux of shape p and filling with the numbers from 0 to n-1.
standardTableaux -- see standardTableaux(Partition) -- the list of standard tableaux of shape p
tableauList -- see tableauList(Partition,ZZ) -- the constructor for the type TableauList
tabloids -- see tabloids(Partition) -- the list of tabloids for a given partition

Methods that use an object of class TableauList :

addTableau(TableauList,List) -- see addTableau(TableauList,YoungTableau) -- adds a Young Tableau in the list
addTableau(TableauList,YoungTableau) -- adds a Young Tableau in the list
higherSpechtPolynomials(YoungTableau,TableauList,PolynomialRing) -- see higherSpechtPolynomials -- a method that gives sets of higher Specht polynomials
matrixRepresentation(List,TableauList) -- see matrixRepresentation -- the matrix representation of a permutation in the Specht Module
matrixRepresentation(TableauList) -- see matrixRepresentation -- the matrix representation of a permutation in the Specht Module
net(TableauList)
TableauList _ ZZ -- a method that retrieves the tableaux from the list
toListOfTableaux(TableauList) -- converts an object of type TableauList into a list of YoungTableau objects

For the programmer

The object TableauList is a type, with ancestor classes MutableHashTable < HashTable < Thing.