Safe Haskell	None
Language	Haskell2010

Math.Combinat.Partitions.Skew

Contents

Basics
Listing skew partitions
ASCII

Description

Skew partitions.

Skew partitions are the difference of two integer partitions, denoted by lambda/mu.

For example

mkSkewPartition (Partition [9,7,3,2,2,1] , Partition [5,3,2,1])

creates the skew partition (9,7,3,2,2,1) / (5,3,2,1), which looks like

Synopsis

newtype SkewPartition = SkewPartition [(Int, Int)]
mkSkewPartition :: (Partition, Partition) -> SkewPartition
safeSkewPartition :: (Partition, Partition) -> Maybe SkewPartition
skewPartitionWeight :: SkewPartition -> Int
normalizeSkewPartition :: SkewPartition -> SkewPartition
fromSkewPartition :: SkewPartition -> (Partition, Partition)
outerPartition :: SkewPartition -> Partition
innerPartition :: SkewPartition -> Partition
dualSkewPartition :: SkewPartition -> SkewPartition
skewPartitionElements :: SkewPartition -> [(Int, Int)]
skewPartitionsWithOuterShape :: Partition -> Int -> [SkewPartition]
allSkewPartitionsWithOuterShape :: Partition -> [SkewPartition]
skewPartitionsWithInnerShape :: Partition -> Int -> [SkewPartition]
asciiSkewFerrersDiagram :: SkewPartition -> ASCII
asciiSkewFerrersDiagram' :: (Char, Char) -> PartitionConvention -> SkewPartition -> ASCII

Basics

newtype SkewPartition Source #

A skew partition lambda/mu is internally represented by the list [ (mu_i , lambda_i-mu_i) | i<-[1..n] ]

Constructors

SkewPartition [(Int, Int)]

Instances

Eq SkewPartition Source #
Instance details Defined in Math.Combinat.Partitions.Skew Methods (==) :: SkewPartition -> SkewPartition -> Bool # (/=) :: SkewPartition -> SkewPartition -> Bool #
Ord SkewPartition Source #
Instance details Defined in Math.Combinat.Partitions.Skew Methods compare :: SkewPartition -> SkewPartition -> Ordering # (<) :: SkewPartition -> SkewPartition -> Bool # (<=) :: SkewPartition -> SkewPartition -> Bool # (>) :: SkewPartition -> SkewPartition -> Bool # (>=) :: SkewPartition -> SkewPartition -> Bool # max :: SkewPartition -> SkewPartition -> SkewPartition # min :: SkewPartition -> SkewPartition -> SkewPartition #
Show SkewPartition Source #
Instance details Defined in Math.Combinat.Partitions.Skew Methods showsPrec :: Int -> SkewPartition -> ShowS # show :: SkewPartition -> String # showList :: [SkewPartition] -> ShowS #
HasDuality SkewPartition Source #
Instance details Defined in Math.Combinat.Partitions.Skew Methods dual :: SkewPartition -> SkewPartition Source #
HasWeight SkewPartition Source #
Instance details Defined in Math.Combinat.Partitions.Skew Methods weight :: SkewPartition -> Int Source #
DrawASCII SkewPartition Source #
Instance details Defined in Math.Combinat.Partitions.Skew Methods ascii :: SkewPartition -> ASCII Source #
HasShape (SkewTableau a) SkewPartition Source #
Instance details Defined in Math.Combinat.Tableaux.Skew Methods shape :: SkewTableau a -> SkewPartition Source #

mkSkewPartition :: (Partition, Partition) -> SkewPartition Source #

mkSkewPartition (lambda,mu) creates the skew partition lambda/mu. Throws an error if mu is not a sub-partition of lambda.

safeSkewPartition :: (Partition, Partition) -> Maybe SkewPartition Source #

Returns Nothing if mu is not a sub-partition of lambda.

skewPartitionWeight :: SkewPartition -> Int Source #

The weight of a skew partition is the weight of the outer partition minus the the weight of the inner partition (that is, the number of boxes present).

normalizeSkewPartition :: SkewPartition -> SkewPartition Source #

This function "cuts off" the "uninteresting parts" of a skew partition

fromSkewPartition :: SkewPartition -> (Partition, Partition) Source #

Returns the outer and inner partition of a skew partition, respectively:

mkSkewPartition . fromSkewPartition == id

outerPartition :: SkewPartition -> Partition Source #

The lambda part of lambda/mu

innerPartition :: SkewPartition -> Partition Source #

The mu part of lambda/mu

dualSkewPartition :: SkewPartition -> SkewPartition Source #

The dual skew partition (that is, the mirror image to the main diagonal)

skewPartitionElements :: SkewPartition -> [(Int, Int)] Source #

See "partitionElements"

Listing skew partitions

skewPartitionsWithOuterShape :: Partition -> Int -> [SkewPartition] Source #

Lists all skew partitions with the given outer shape and given (skew) weight

allSkewPartitionsWithOuterShape :: Partition -> [SkewPartition] Source #

Lists all skew partitions with the given outer shape and any (skew) weight

skewPartitionsWithInnerShape :: Partition -> Int -> [SkewPartition] Source #

Lists all skew partitions with the given inner shape and given (skew) weight

ASCII

asciiSkewFerrersDiagram :: SkewPartition -> ASCII Source #

asciiSkewFerrersDiagram' :: (Char, Char) -> PartitionConvention -> SkewPartition -> ASCII Source #