SkewTableau -- a type of HashTable representing a skew Young tableau

Description

An object of type SkewTableau 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 = skewTableau(lam,mu,entryList)

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

o4 : SkewTableau

Types of SkewTableau:

YoungTableau -- a type of HashTable representing a (nonskew) Young tableau

Functions and methods returning an object of class SkewTableau:

applyEntries -- apply a function to all entries in the tableau
applyPositions -- apply a function to all positions of boxes in a tableau
shift -- shift a tableau
skewTableau -- constructor for type SkewTableau
unshift -- unshift a tableau
verticalConcatenate -- vertical concatenation of a list of tableaux

Methods that use an object of class SkewTableau:

applyEntries(SkewTableau,Function) -- see applyEntries -- apply a function to all entries in the tableau
applyPositions(SkewTableau,Function) -- see applyPositions -- apply a function to all positions of boxes in a tableau
columnEntries(SkewTableau,ZZ) -- see columnEntries -- get the entries in a column.
columnEntries(ZZ,SkewTableau) -- see columnEntries -- get the entries in a column.
columnRange(SkewTableau) -- see columnRange -- the range of column indices of a tableau.
components(SkewTableau) -- get the connected components of a tableau
conjugate(SkewTableau) -- conjugate a tableau
entries(SkewTableau) -- the filling of a skew tableau
ferrersDiagram(SkewTableau) -- see ferrersDiagram -- a net of the Ferrers diagram
hookLength(Sequence,SkewTableau) -- see hookLength -- compute the hook length of a box of a tableau
isNonnegative(SkewTableau) -- see isNonnegative -- check if shapes are nonnegative
isWeaklyDecreasing(SkewTableau) -- see isWeaklyDecreasing -- check if shapes are weakly decreasing
numColumns(SkewTableau) -- the number of columns in a tableau
numRows(SkewTableau) -- the number of rows in a tableau
positionList(SkewTableau) -- see positionList -- get the positions of all the boxes in a tableau
rowEntries(SkewTableau,ZZ) -- see rowEntries -- get the entries in a row.
rowEntries(ZZ,SkewTableau) -- see rowEntries -- get the entries in a row.
rowRange(SkewTableau) -- see rowRange -- the range of row indices of a tableau.
shift(SkewTableau) -- see shift -- shift a tableau
shift(SkewTableau,ZZ) -- see shift -- shift a tableau
size(SkewTableau) -- the number of boxes in a skew tableau
skewShape(SkewTableau) -- see skewShape -- the shape of a skew tableau
net(SkewTableau)
SkewTableau ++ SkewTableau -- direct sum of tableaux
SkewTableau ^ ZZ -- get the entries in a row.
SkewTableau _ Sequence -- get the entry at a specific position.
SkewTableau _ ZZ -- get the entries in a column.
SkewTableau || SkewTableau -- vertical concatenation of two tableaux
tex(SkewTableau) -- LaTeX output for a skew tableau
toIndex(Sequence,SkewTableau) -- see toIndex -- get the index of a box, given its position.
toIndex(SkewTableau,Sequence) -- see toIndex -- get the index of a box, given its position.
toPosition(SkewTableau,ZZ) -- see toPosition -- get the position of a box, given its index.
toPosition(ZZ,SkewTableau) -- see toPosition -- get the position of a box, given its index.
unshift(SkewTableau) -- see unshift -- unshift a tableau
unshift(SkewTableau,ZZ) -- see unshift -- unshift a tableau
youngDiagram(SkewTableau) -- see youngDiagram -- a net of the Young diagram

For the programmer

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