combinat-0.2.8.2: Generate and manipulate various combinatorial objects.

Math.Combinat.Tableaux.Skew

Description

Skew tableaux are skew partitions filled with numbers.

For example:

Synopsis

# Basics

newtype SkewTableau a Source #

A skew tableau is represented by a list of offsets and entries

Constructors

 SkewTableau [(Int, [a])]

Instances

 Source # Methodsfmap :: (a -> b) -> SkewTableau a -> SkewTableau b #(<\$) :: a -> SkewTableau b -> SkewTableau a # Eq a => Eq (SkewTableau a) Source # Methods(==) :: SkewTableau a -> SkewTableau a -> Bool #(/=) :: SkewTableau a -> SkewTableau a -> Bool # Ord a => Ord (SkewTableau a) Source # Methodscompare :: SkewTableau a -> SkewTableau a -> Ordering #(<) :: SkewTableau a -> SkewTableau a -> Bool #(<=) :: SkewTableau a -> SkewTableau a -> Bool #(>) :: SkewTableau a -> SkewTableau a -> Bool #(>=) :: SkewTableau a -> SkewTableau a -> Bool #max :: SkewTableau a -> SkewTableau a -> SkewTableau a #min :: SkewTableau a -> SkewTableau a -> SkewTableau a # Show a => Show (SkewTableau a) Source # MethodsshowsPrec :: Int -> SkewTableau a -> ShowS #show :: SkewTableau a -> String #showList :: [SkewTableau a] -> ShowS # Show a => DrawASCII (SkewTableau a) Source # Methods Source # Methods Source # Methods Source # Methods

The shape of a skew tableau

The weight of a tableau is the weight of its shape, or the number of entries

dualSkewTableau :: forall a. SkewTableau a -> SkewTableau a Source #

The dual of a skew tableau, that is, its mirror image to the main diagonal

# Semistandard tableau

A tableau is semistandard if its entries are weekly increasing horizontally and strictly increasing vertically

A tableau is standard if it is semistandard and its content is exactly [1..n], where n is the weight.

All semi-standard skew tableaux filled with the numbers [1..n]

# ASCII

ASCII drawing of a skew tableau (using the English notation)

Arguments

 :: Show a => String string representing the elements of the inner (unfilled) partition -> PartitionConvention orientation -> SkewTableau a -> ASCII

# Row / column words

skewTableauRowWord :: SkewTableau a -> [a] Source #

The reversed (right-to-left) rows, concatenated

skewTableauColumnWord :: SkewTableau a -> [a] Source #

The reversed (bottom-to-top) columns, concatenated

Fills a skew partition with content, in row word order

Fills a skew partition with content, in column word order

If the skew tableau's row word is a lattice word, we can make a partition from its content