combinat-0.2.10.0: Generate and manipulate various combinatorial objects.
Safe HaskellNone
LanguageHaskell2010

Math.Combinat.Partitions.Plane

Description

Plane partitions. See eg. http://en.wikipedia.org/wiki/Plane_partition

Plane partitions are encoded as lists of lists of Z heights. For example the plane partition in the picture

is encoded as

PlanePart [ [5,4,3,3,1]
          , [4,4,2,1]
          , [3,2]
          , [2,1]
          , [1]
          , [1]
          ]
Synopsis

the type of plane partitions

newtype PlanePart Source #

A plane partition encoded as a tablaeu (the "Z" heights are the numbers)

Constructors

PlanePart [[Int]] 

Instances

Instances details
Eq PlanePart Source # 
Instance details

Defined in Math.Combinat.Partitions.Plane

Methods

(==) :: PlanePart -> PlanePart -> Bool #

(/=) :: PlanePart -> PlanePart -> Bool #

Ord PlanePart Source # 
Instance details

Defined in Math.Combinat.Partitions.Plane

Methods

compare :: PlanePart -> PlanePart -> Ordering #

(<) :: PlanePart -> PlanePart -> Bool #

(<=) :: PlanePart -> PlanePart -> Bool #

(>) :: PlanePart -> PlanePart -> Bool #

(>=) :: PlanePart -> PlanePart -> Bool #

max :: PlanePart -> PlanePart -> PlanePart #

min :: PlanePart -> PlanePart -> PlanePart #

Show PlanePart Source # 
Instance details

Defined in Math.Combinat.Partitions.Plane

Methods

showsPrec :: Int -> PlanePart -> ShowS #

show :: PlanePart -> String #

showList :: [PlanePart] -> ShowS #

HasWeight PlanePart Source # 
Instance details

Defined in Math.Combinat.Partitions.Plane

Methods

weight :: PlanePart -> Int Source #

CanBeEmpty PlanePart Source # 
Instance details

Defined in Math.Combinat.Partitions.Plane

Methods

isEmpty :: PlanePart -> Bool Source #

empty :: PlanePart Source #

fromPlanePart :: PlanePart -> [[Int]] Source #

isValidPlanePart :: [[Int]] -> Bool Source #

toPlanePart :: [[Int]] -> PlanePart Source #

Throws an exception if the input is not a plane partition

planePartShape :: PlanePart -> Partition Source #

The XY projected shape of a plane partition, as an integer partition

planePartZHeight :: PlanePart -> Int Source #

The Z height of a plane partition

planePartWeight :: PlanePart -> Int Source #

constructing plane partitions

singleLayer :: Partition -> PlanePart Source #

stackLayers :: [Partition] -> PlanePart Source #

Stacks layers of partitions into a plane partition. Throws an exception if they do not form a plane partition.

unsafeStackLayers :: [Partition] -> PlanePart Source #

Stacks layers of partitions into a plane partition. This is unsafe in the sense that we don't check that the partitions fit on the top of each other.

planePartLayers :: PlanePart -> [Partition] Source #

The "layers" of a plane partition (in direction Z). We should have

unsafeStackLayers (planePartLayers pp) == pp

generating plane partitions

planePartitions :: Int -> [PlanePart] Source #

Plane partitions of a given weight