Tableaux : Table of Contents

• Tableaux -- a package for computing with Young tableaux
• allSemistandardTableaux -- list all semistandard Young tableaux of a given shape
• allStandardTableaux -- list all standard Young tableaux of a given shape
• allSubPartitions -- list all partitions whose Young diagrams are contained in another
• allTabloids -- list all tabloids of a given shape
• applyEntries -- apply a function to all entries in the tableau
• applyPositions -- apply a function to all positions of boxes in a tableau
• boxContent -- compute the content of a box of a tableau
• columnEntries -- get the entries in a column
• columnRange -- the range of column indices of a tableau
• columnStabilizer -- the column stabilizer of a tableau
• components(YoungTableau) -- get the connected components of a tableau
• conjugate(YoungTableau) -- conjugate a tableau
• drawInnerShape -- option to draw the inner shape of a tableau
• entries(YoungTableau) -- the filling of a tableau
• ferrersDiagram -- a net of the Ferrers diagram
• hookLength -- compute the hook length of a box of a tableau
• horizontalNet -- multiple nets concatenated horizontally
• innerShape -- the inner shape of a (skew) Young tableau
• isCorner -- checks if a box is a corner of a tableau
• isNonnegative -- check if shapes are nonnegative
• isSemistandard -- checks if a Young tableau is semistandard
• isSkew -- checks if a Young tableau is skew
• isStandard -- checks if a Young tableau is standard
• isWeaklyDecreasing -- check if shapes are weakly decreasing
• MutableYoungTableau -- a type of HashTable representing a Young tableau, with mutable entries
• mutableYoungTableau -- constructor for type MutableYoungTableau
• MutableYoungTableau _ Sequence = Thing -- change an entry of a mutable Young tableau
• numColumns(YoungTableau) -- the number of columns in a tableau
• numRows(YoungTableau) -- the number of rows in a tableau
• numSemistandardTableaux -- compute the number of semistandard Young tableaux of a given shape
• numStandardTableaux -- compute the number of standard Young tableaux of a given shape
• numTabloids -- compute the number of tabloids of a given shape
• outerShape -- the outer shape of a (skew) Young tableau
• positionList -- get the positions of all the boxes in a tableau
• randomSemistandardTableau -- get a random semistandard Young Tableau
• randomStandardTableau -- get a random standard Young Tableau
• randomTabloid -- get a random tabloid
• readingWord -- get the reading word of a tableau
• representative -- get a canonical representative of a tabloid
• rowEntries -- get the entries in a row
• rowRange -- the range of row indices of a tableau
• rowStabilizer -- the row stabilizer of a tableau
• shape -- the shape of a Young tableau
• shift -- shift a tableau
• size(YoungTableau) -- the number of boxes in a tableau
• skewShape -- the shape of a skew tableau
• standardize -- standardize the lengths of a pair of partitions
• Tabloid -- a type of HashTable representing a Young tabloid
• tabloid -- constructor for type Tabloid
• Tabloid == Tabloid -- check if two tabloids are equal
• tex(YoungTableau) -- LaTeX output for a tableau
• toIndex -- get the index of a box, given its position
• toList(Tabloid) -- list representation of a tabloid
• toPartitionChain -- decompose a tableau into a chain of partitions
• toPosition -- get the position of a box, given its index
• unshift -- unshift a tableau
• verticalConcatenate -- vertical concatenation of a list of tableaux
• verticalNet -- multiple nets concatenated vertically
• youngDiagram -- a net of the Young diagram
• YoungTableau -- a type of HashTable representing a Young tableau
• youngTableau -- constructor for type YoungTableau
• YoungTableau ++ YoungTableau -- direct sum of tableaux
• YoungTableau == YoungTableau -- check if two Young tableaux are equal
• YoungTableau ^ ZZ -- get the entries in a row
• YoungTableau _ Sequence -- get the entry at a specific position
• YoungTableau _ ZZ -- get the entries in a column
• YoungTableau || YoungTableau -- vertical concatenation of two tableaux