Math.Combinat.Tableaux.Skew

Skew tableaux are skew partitions filled with numbers.

Documentation

newtype SkewTableau a

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

Constructors

SkewTableau [(Int, [a])]

Instances

Functor SkewTableau

Eq a => Eq (SkewTableau a)

Ord a => Ord (SkewTableau a)

Show a => Show (SkewTableau a)

Show a => DrawASCII (SkewTableau a)

skewShape :: SkewTableau a -> SkewPartition

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

semiStandardSkewTableaux :: Int -> SkewPartition -> [SkewTableau Int]

Semi-standard skew tableaux filled with numbers [1..n]

asciiSkewTableau :: Show a => SkewTableau a -> ASCII

asciiSkewTableau'

Arguments

:: Show a

=> String

string representing the elements of the inner (unfilled) partition

-> PartitionConvention

-> SkewTableau a

-> ASCII

skewTableauRowWord :: SkewTableau a -> [a]

The reversed rows, concatenated

skewTableauColumnWord :: SkewTableau a -> [a]

The reversed rows, concatenated

fillSkewPartitionWithRowWord :: SkewPartition -> [a] -> SkewTableau a

Fills a skew partition with content, in row word order

fillSkewPartitionWithColumnWord :: SkewPartition -> [a] -> SkewTableau a

Fills a skew partition with content, in column word order

skewTableauRowContent :: SkewTableau Int -> Maybe Partition

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