Safe Haskell  None 

Language  Haskell2010 
Ribbons (also called border strips, skew hooks, skew rim hooks, etc...).
Ribbons are skew partitions that are 1) connected, 2) do not contain 2x2 blocks. Intuitively, they are 1box wide continuous strips on the boundary.
An alternative definition that they are skew partitions whose projection to the diagonal line is a continuous segment of width 1.
Synopsis
 outerCorners :: Partition > [(Int, Int)]
 extendedInnerCorners :: Partition > [(Int, Int)]
 extendedCornerSequence :: Partition > [(Int, Int)]
 innerCornerBoxes :: Partition > [(Int, Int)]
 outerCornerBoxes :: Partition > [(Int, Int)]
 cornerBoxSequence :: Partition > [(Int, Int)]
 innerCornerBoxesNaive :: Partition > [(Int, Int)]
 outerCornerBoxesNaive :: Partition > [(Int, Int)]
 isRibbon :: SkewPartition > Bool
 toRibbon :: SkewPartition > Maybe Ribbon
 data Ribbon = Ribbon {}
 innerRibbons :: Partition > [Ribbon]
 innerRibbonsOfLength :: Partition > Int > [Ribbon]
 listHooks :: Int > [Partition]
 outerRibbonsOfLength :: Partition > Int > [Ribbon]
 innerRibbonsNaive :: Partition > [Ribbon]
 innerRibbonsOfLengthNaive :: Partition > Int > [Ribbon]
 outerRibbonsOfLengthNaive :: Partition > Int > [Ribbon]
 data BorderBox = BorderBox {
 _canStartStrip :: !Bool
 _canEndStrip :: !Bool
 _yCoord :: !Int
 _xCoord :: !Int
 annotatedInnerBorderStrip :: Partition > [BorderBox]
 annotatedOuterBorderStrip :: Partition > [BorderBox]
Corners (TODO: move to Partitions  but we also want to refactor that)
extendedInnerCorners :: Partition > [(Int, Int)] Source #
The coordinates of the inner corners, including the two on the two coordinate
axes. For the partition [5,4,1]
the result should be [(0,5),(1,4),(2,1),(3,0)]
innerCornerBoxes :: Partition > [(Int, Int)] Source #
The inner corner boxes of the partition. Coordinates are counted from 1
(cf.the elements
function), and the first coordinate is the row, the second
the column (in English notation).
For the partition [5,4,1]
the result should be [(1,4),(2,1)]
innerCornerBoxes lambda == (tail $ init $ extendedInnerCorners lambda)
outerCornerBoxes :: Partition > [(Int, Int)] Source #
The outer corner boxes of the partition. Coordinates are counted from 1
(cf.the elements
function), and the first coordinate is the row, the second
the column (in English notation).
For the partition [5,4,1]
the result should be [(1,5),(2,4),(3,1)]
cornerBoxSequence :: Partition > [(Int, Int)] Source #
The outer and inner corner boxes interleaved, so together they form the turning points of the full border strip
innerCornerBoxesNaive :: Partition > [(Int, Int)] Source #
Naive (and very slow) implementation of innerCornerBoxes
, for testing purposes
outerCornerBoxesNaive :: Partition > [(Int, Int)] Source #
Naive (and very slow) implementation of outerCornerBoxes
, for testing purposes
Ribbon
isRibbon :: SkewPartition > Bool Source #
A skew partition is a a ribbon (or border strip) if and only if projected to the diagonals the result is an interval.
Border strips (or ribbons) are defined to be skew partitions which are connected and do not contain 2x2 blocks.
The length of a border strip is the number of boxes it contains, and its height is defined to be one less than the number of rows (in English notation) it occupies. The width is defined symmetrically to be one less than the number of columns it occupies.
Inner border strips
innerRibbons :: Partition > [Ribbon] Source #
Ribbons (or border strips) are defined to be skew partitions which are connected and do not contain 2x2 blocks. This function returns the border strips whose outer partition is the given one.
innerRibbonsOfLength :: Partition > Int > [Ribbon] Source #
Inner border strips (or ribbons) of the given length
Outer border strips
outerRibbonsOfLength :: Partition > Int > [Ribbon] Source #
Outer border strips (or ribbons) of the given length
Naive implementations (for testing)
innerRibbonsNaive :: Partition > [Ribbon] Source #
Naive (and slow) implementation listing all inner border strips
innerRibbonsOfLengthNaive :: Partition > Int > [Ribbon] Source #
Naive (and slow) implementation listing all inner border strips of the given length
outerRibbonsOfLengthNaive :: Partition > Int > [Ribbon] Source #
Naive (and slow) implementation listing all outer border strips of the given length
Annotated borders
A box on the border of a partition
BorderBox  

annotatedInnerBorderStrip :: Partition > [BorderBox] Source #
The boxes of the full inner border strip, annotated with whether a border strip can start or end there.
annotatedOuterBorderStrip :: Partition > [BorderBox] Source #
The boxes of the full outer border strip, annotated with whether a border strip can start or end there.