SpechtModule : Table of Contents

• SpechtModule -- a package for constructing Specht Modules
• addTableau(TableauList,YoungTableau) -- adds a Young Tableau in the list
• AsExpression -- an optional argument that returns polynomials as expressions
• cardinalityOfConjugacyClass(Partition) -- the size of the conjugacy classes of S_n
• CharacterTable -- the class of character tables
• characterTable -- returns the character table of the symmetric group
• CharacterTable _ Sequence -- retrieves an entry from the character table
• CharacterTable _ Sequence = Thing -- modifies an entry from the character table
• columnStabilizer(YoungTableau) -- the column stabilizer of the tableau
• conjugacyClass(List) -- the conjugacy class of a permutation
• cycleDecomposition(List) -- the cycle decomposition of a permutation
• elementarySymmetricPolynomials(PolynomialRing) -- the elementary symmetric polynomials
• entries(YoungTableau) -- returns the filling of the tableau
• firstRowDescent(YoungTableau) -- retrieves the first row descent of a Young tableau
• garnirElement -- a SpechtModuleElement that is equal to zero
• generalizedVandermondeMatrix(List,List,PolynomialRing) -- the method for calculating generalized Vandermonde matrices
• generatePermutationGroup(List) -- a method for generating a permutation group given a set of generators
• higherSpechtPolynomial(YoungTableau,YoungTableau,PolynomialRing) -- the higher Specht polynomial index by the pair of standard tableaux (S,T)
• higherSpechtPolynomials -- a method that gives sets of higher Specht polynomials
• hookLengthFormula(Partition) -- a formula for the number of standard tableaux
• indexMonomial(YoungTableau,YoungTableau,PolynomialRing) -- a monomial that represents an index tableau
• indexTableau(YoungTableau) -- the index tableau for a given tableau
• innerProduct(ZZ,MutableMatrix,MutableMatrix) -- calculates the inner product for the characters of S_n
• listToTableau(List) -- constructs a Young Tableau from a doubly nested list of numbers
• matrixRepresentation -- the matrix representation of a permutation in the Specht Module
• multinomial -- a formula for the multinomial coefficient
• numColumns(YoungTableau) -- returns the number of columns of a tableau
• numRows(YoungTableau) -- returns the number of rows of a tableau
• permutationMatrix(List) -- a permutation matrix generator
• permutationSign -- the sign of a permutation
• permutePolynomial -- permutes a RingElement or a PolynomialExpression of RingElements
• powerSumSymmetricPolynomials(PolynomialRing) -- the power sum symmetric polynomials
• readingWord(YoungTableau) -- gives the reading word of a given tableau
• representationMultiplicity -- the number of secondary invariants in a given irreducible representation
• Robust -- an optional argument for specifying the algorithm for calculating higherSpechtPolynomials
• rowPermutationTableaux(YoungTableau) -- the list of row permutations without repetitions in columns
• rowStabilizer(YoungTableau) -- the row stabilizer of the tableau
• schurPolynomial(List,Partition,PolynomialRing) -- a method for constructing Schur polynomials
• secondaryInvariants(List,PolynomialRing) -- the set of secondaryInvariants of a permutation group
• semistandardTableaux(Partition,ZZ) -- the list of semistandard tableaux of shape p and filling with the numbers from 0 to n-1.
• size(YoungTableau) -- returns the number of cells of a tableau
• sortColumnsTableau(SpechtModuleElement) -- a method for sorting the columns of the tableaux in a SpechtModuleElement
• sortColumnsTableau(YoungTableau) -- a method for
• SpechtModuleElement -- the class of Specht Module elements
• spechtModuleElement -- the constructor for the class SpechtModuleElement
• spechtPolynomial(YoungTableau,PolynomialRing) -- the Specht polynomial indexed by a standard tableau
• spechtPolynomials(Partition,PolynomialRing) -- the set of all Specht polynomial indexed by standard tableaux of shape p
• standardTableaux(Partition) -- the list of standard tableaux of shape p
• straighteningAlgorithm -- an algorithm for expressing any polytabloid as linear combinations of standard polytabloids
• TableauList -- the class of list of tableaux
• TableauList _ ZZ -- a method that retrieves the tableaux from the list
• tableauList(Partition,ZZ) -- the constructor for the type TableauList
• tableauToList(YoungTableau) -- converts a YoungTableau to list form
• tabloids(Partition) -- the list of tabloids for a given partition
• toListOfTableaux(TableauList) -- converts an object of type TableauList into a list of YoungTableau objects
• vandermondeDeterminant -- the vandermonde determinant for a set of generators of a ring
• YoungTableau -- the class of Young Tableaux
• youngTableau -- the constructor method for the class YoungTableau
• YoungTableau == YoungTableau -- checks whether 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