YoungTableau -- a type of HashTable representing a Young tableau

Description

An object of type YoungTableau is a hash table containing two shapes of type Partition, and a list of box entries. The entries may have any type, except for null objects.

The inner and outer shapes, $\lambda$ and $\mu$ respectively, can be any sequence of integers. In particular, it accepts negative parts, compositions, rows where $\lambda_i < \mu_i$, and compositions where $\ell(\lambda)\neq\ell(\mu)$.

i1 : lam = new Partition from {4,3,2}

o1 = Partition{4, 3, 2}

o1 : Partition

i2 : mu = new Partition from {3,1}

o2 = Partition{3, 1}

o2 : Partition

i3 : entryList = {1,2,3,3,9}

o3 = {1, 2, 3, 3, 9}

o3 : List

i4 : T = youngTableau(lam,mu,entryList)

                 ┌───┐
o4 =             │ 1 │
         ┌───┬───┼───┘
         │ 2 │ 3 │    
     ┌───┼───┼───┘    
     │ 3 │ 9 │        
     └───┴───┘        

o4 : YoungTableau

Types of YoungTableau:

MutableYoungTableau -- a type of HashTable representing a Young tableau, with mutable entries
Tabloid -- a type of HashTable representing a Young tabloid

Functions and methods returning an object of class YoungTableau:

applyEntries -- apply a function to all entries in the tableau
applyPositions -- apply a function to all positions of boxes in a tableau
randomSemistandardTableau -- get a random semistandard Young Tableau
randomStandardTableau -- get a random standard Young Tableau
shift -- shift a tableau
unshift -- unshift a tableau
verticalConcatenate -- vertical concatenation of a list of tableaux
youngTableau -- constructor for type YoungTableau

Methods that use an object of class YoungTableau:

applyEntries(YoungTableau,Function) -- see applyEntries -- apply a function to all entries in the tableau
applyPositions(YoungTableau,Function) -- see applyPositions -- apply a function to all positions of boxes in a tableau
columnEntries(YoungTableau,ZZ) -- see columnEntries -- get the entries in a column
columnEntries(ZZ,YoungTableau) -- see columnEntries -- get the entries in a column
columnRange(YoungTableau) -- see columnRange -- the range of column indices of a tableau
columnStabilizer(YoungTableau) -- see columnStabilizer -- the column stabilizer of a tableau
components(YoungTableau) -- get the connected components of a tableau
conjugate(YoungTableau) -- conjugate a tableau
entries(YoungTableau) -- the filling of a tableau
ferrersDiagram(YoungTableau) -- see ferrersDiagram -- a net of the Ferrers diagram
hookLength(Sequence,YoungTableau) -- see hookLength -- compute the hook length of a box of a tableau
innerShape(YoungTableau) -- see innerShape -- the inner shape of a (skew) Young tableau
isCorner(Sequence,YoungTableau) -- see isCorner -- checks if a box is a corner of a tableau
isNonnegative(YoungTableau) -- see isNonnegative -- check if shapes are nonnegative
isSemistandard(YoungTableau) -- see isSemistandard -- checks if a Young tableau is semistandard
isSkew(YoungTableau) -- see isSkew -- checks if a Young tableau is skew
isStandard(YoungTableau) -- see isStandard -- checks if a Young tableau is standard
isWeaklyDecreasing(YoungTableau) -- see isWeaklyDecreasing -- check if shapes are weakly decreasing
numColumns(YoungTableau) -- the number of columns in a tableau
numRows(YoungTableau) -- the number of rows in a tableau
outerShape(YoungTableau) -- see outerShape -- the outer shape of a (skew) Young tableau
positionList(YoungTableau) -- see positionList -- get the positions of all the boxes in a tableau
positionList(YoungTableau,Function) -- see positionList -- get the positions of all the boxes in a tableau
readingWord(YoungTableau) -- see readingWord -- get the reading word of a tableau
rowEntries(YoungTableau,ZZ) -- see rowEntries -- get the entries in a row
rowEntries(ZZ,YoungTableau) -- see rowEntries -- get the entries in a row
rowRange(YoungTableau) -- see rowRange -- the range of row indices of a tableau
rowStabilizer(YoungTableau) -- see rowStabilizer -- the row stabilizer of a tableau
shape(YoungTableau) -- see shape -- the shape of a Young tableau
shift(YoungTableau) -- see shift -- shift a tableau
shift(YoungTableau,ZZ) -- see shift -- shift a tableau
size(YoungTableau) -- the number of boxes in a tableau
skewShape(YoungTableau) -- see skewShape -- the shape of a skew tableau
tabloid(YoungTableau) -- see tabloid -- constructor for type Tabloid
tex(YoungTableau) -- LaTeX output for a tableau
toIndex(Sequence,YoungTableau) -- see toIndex -- get the index of a box, given its position
toIndex(YoungTableau,Sequence) -- see toIndex -- get the index of a box, given its position
toPartitionChain(YoungTableau) -- see toPartitionChain -- decompose a tableau into a chain of partitions
toPosition(YoungTableau,ZZ) -- see toPosition -- get the position of a box, given its index
toPosition(ZZ,YoungTableau) -- see toPosition -- get the position of a box, given its index
unshift(YoungTableau) -- see unshift -- unshift a tableau
unshift(YoungTableau,ZZ) -- see unshift -- unshift a tableau
youngDiagram(YoungTableau) -- see youngDiagram -- a net of the Young diagram
net(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

For the programmer

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