YoungTableau -- the class of Young Tableaux

i1 : p = new Partition from {3,2}

o1 = Partition{3, 2}

o1 : Partition

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

o2 = | 1 0 2 |
     | 3 4 |

o2 : YoungTableau

i3 : peek y

o3 = YoungTableau{partition => Partition{3, 2}  }
                  values => MutableList{...5...}

Functions and methods returning an object of class YoungTableau :

• "listToTableau" -- see listToTableau(List) -- constructs a Young Tableau from a doubly nested list of numbers
• youngTableau -- the constructor method for the class YoungTableau

Methods that use an object of class YoungTableau :

• addTableau(TableauList,YoungTableau) -- adds a Young Tableau in the list
• columnStabilizer(YoungTableau) -- the column stabilizer of the tableau
• entries(YoungTableau) -- returns the filling of the tableau
• firstRowDescent(YoungTableau) -- retrieves the first row descent of a young tableau
• "garnirElement(YoungTableau)" -- see garnirElement -- a SpechtModuleElement that is equal to zero
• "garnirElement(YoungTableau,ZZ)" -- see garnirElement -- a SpechtModuleElement that is equal to zero
• "garnirElement(YoungTableau,ZZ,ZZ,ZZ)" -- see garnirElement -- a SpechtModuleElement that is equal to zero
• higherSpechtPolynomial(YoungTableau,YoungTableau,PolynomialRing) -- the higher Specht polynomial index by the pair of standard tableaux (S,T)
• "higherSpechtPolynomials(YoungTableau,PolynomialRing)" -- see higherSpechtPolynomials -- a method that gives sets of higher Specht polynomials
• "higherSpechtPolynomials(YoungTableau,TableauList,PolynomialRing)" -- see higherSpechtPolynomials -- a method that gives sets of higher Specht polynomials
• indexMonomial(YoungTableau,YoungTableau,PolynomialRing) -- a monomial that represents an index tableau
• indexTableau(YoungTableau) -- the index tableau for a given tableau
• numColumns(YoungTableau) -- returns the number of columns of a tableau
• numRows(YoungTableau) -- returns the number of rows of a tableau
• readingWord(YoungTableau) -- gives the reading word of a given tableau
• rowPermutationTableaux(YoungTableau) -- the list of row permutations without repetitions in columns
• rowStabilizer(YoungTableau) -- the row stabilizer of the tableau
• size(YoungTableau) -- returns the number of cells of a tableau
• sortColumnsTableau(YoungTableau) -- a method for
• "spechtModuleElement(YoungTableau)" -- see spechtModuleElement -- the constructor for the class SpechtModuleElement
• "spechtModuleElement(YoungTableau,QQ)" -- see spechtModuleElement -- the constructor for the class SpechtModuleElement
• "spechtModuleElement(YoungTableau,ZZ)" -- see spechtModuleElement -- the constructor for the class SpechtModuleElement
• spechtPolynomial(YoungTableau,PolynomialRing) -- the Specht polynomial indexed by a standard tableau
• "straighteningAlgorithm(YoungTableau)" -- see straighteningAlgorithm -- an algorithm for expressing any polytabloid as linear combinations of standard polytabloids
• "straighteningAlgorithm(YoungTableau,ZZ)" -- see straighteningAlgorithm -- an algorithm for expressing any polytabloid as linear combinations of standard polytabloids
• tableauToList(YoungTableau) -- converts a YoungTableau to list form
• "net(YoungTableau)"
• YoungTableau == YoungTableau -- checks wheter two tableaux are equivalent
• YoungTableau ? YoungTableau -- an order of YoungTableaux
• YoungTableau ^ ZZ -- retrieves a row from a Young Tableau
• YoungTableau _ Sequence -- retrieves the entry in cell (a,b) from a Young Tableau
• YoungTableau _ Sequence = Thing -- changes the entry in cell (a,b) from a Young Tableau
• YoungTableau _ ZZ -- retrieves a column from a Young Tableau
• youngTableau(YoungTableau) -- creates a copy of a YoungTableau object

For the programmer

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