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