Math.Combinat.Partitions.Plane

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]
          ]

the type of plane partitions

newtype PlanePart

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

Constructors

PlanePart [[Int]]

Instances

Eq PlanePart

Ord PlanePart

Show PlanePart

HasWeight PlanePart

CanBeEmpty PlanePart

fromPlanePart :: PlanePart -> [[Int]]

isValidPlanePart :: [[Int]] -> Bool

toPlanePart :: [[Int]] -> PlanePart

Throws an exception if the input is not a plane partition

planePartShape :: PlanePart -> Partition

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

planePartZHeight :: PlanePart -> Int

The Z height of a plane partition

planePartWeight :: PlanePart -> Int

constructing plane partitions

singleLayer :: Partition -> PlanePart

stackLayers :: [Partition] -> PlanePart

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

unsafeStackLayers :: [Partition] -> PlanePart

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]

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

unsafeStackLayers (planePartLayers pp) == pp

generating plane partitions

planePartitions :: Int -> [PlanePart]

Plane partitions of a given weight