Safe Haskell	None
Language	Haskell98

Math.Combinatorics.Hypergraph

Description

A module defining a type for hypergraphs.

Synopsis

data Hypergraph a = H [a] [[a]]
hypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a
toHypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a
isUniform :: Ord a => Hypergraph a -> Bool
same :: Eq a => [a] -> Bool
fromGraph :: Graph a -> Hypergraph a
fromDesign :: Ord a => Design a -> Hypergraph a
incidenceGraph :: Ord a => Hypergraph a -> Graph (Either a [a])
incidenceMatrix :: (Eq a1, Num a2) => Hypergraph a1 -> [[a2]]
fromIncidenceMatrix :: (Num a1, Enum a1, Ord a1, Num a2, Eq a2) => [[a2]] -> Hypergraph a1
isPartialLinearSpace :: Ord a => Hypergraph a -> Bool
isProjectivePlane :: Ord a => Hypergraph a -> Bool
isProjectivePlaneTri :: Ord a => Hypergraph a -> Bool
isProjectivePlaneQuad :: Ord a => Hypergraph a -> Bool
isGeneralizedQuadrangle :: Ord a => Hypergraph a -> Bool
grid :: (Ord a, Ord b, Num a, Num b, Enum a, Enum b) => a -> b -> Hypergraph (a, b)
dualGrid :: Integral a => a -> a -> Hypergraph a
isGenQuadrangle' :: Ord a => Hypergraph a -> Bool
isConfiguration :: Ord a => Hypergraph a -> Bool
fanoPlane :: Hypergraph Integer
heawoodGraph :: Graph (Either Integer [Integer])
desarguesConfiguration :: Hypergraph [Integer]
desarguesGraph :: Graph (Either [Integer] [[Integer]])
pappusConfiguration :: Hypergraph Integer
pappusGraph :: Graph (Either Integer [Integer])
coxeterGraph :: Graph [Integer]
duads :: [[Integer]]
synthemes :: [[[Integer]]]
tutteCoxeterGraph :: Graph (Either [Integer] [[Integer]])
intersectionGraph :: Ord a => Hypergraph a -> Graph [a]

Documentation

data Hypergraph a Source #

Constructors

H [a] [[a]]

Instances

Eq a => Eq (Hypergraph a) Source #
Instance details Defined in Math.Combinatorics.Hypergraph Methods (==) :: Hypergraph a -> Hypergraph a -> Bool # (/=) :: Hypergraph a -> Hypergraph a -> Bool #
Ord a => Ord (Hypergraph a) Source #
Instance details Defined in Math.Combinatorics.Hypergraph Methods compare :: Hypergraph a -> Hypergraph a -> Ordering # (<) :: Hypergraph a -> Hypergraph a -> Bool # (<=) :: Hypergraph a -> Hypergraph a -> Bool # (>) :: Hypergraph a -> Hypergraph a -> Bool # (>=) :: Hypergraph a -> Hypergraph a -> Bool # max :: Hypergraph a -> Hypergraph a -> Hypergraph a # min :: Hypergraph a -> Hypergraph a -> Hypergraph a #
Show a => Show (Hypergraph a) Source #
Instance details Defined in Math.Combinatorics.Hypergraph Methods showsPrec :: Int -> Hypergraph a -> ShowS # show :: Hypergraph a -> String # showList :: [Hypergraph a] -> ShowS #

hypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a Source #

toHypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a Source #

isUniform :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph uniform - meaning that all blocks are of the same size

same :: Eq a => [a] -> Bool Source #

fromGraph :: Graph a -> Hypergraph a Source #

fromDesign :: Ord a => Design a -> Hypergraph a Source #

incidenceGraph :: Ord a => Hypergraph a -> Graph (Either a [a]) Source #

incidenceMatrix :: (Eq a1, Num a2) => Hypergraph a1 -> [[a2]] Source #

fromIncidenceMatrix :: (Num a1, Enum a1, Ord a1, Num a2, Eq a2) => [[a2]] -> Hypergraph a1 Source #

isPartialLinearSpace :: Ord a => Hypergraph a -> Bool Source #

isProjectivePlane :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph a projective plane - meaning that any two lines meet in a unique point, and any two points lie on a unique line

isProjectivePlaneTri :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph a projective plane with a triangle. This is a weak non-degeneracy condition, which eliminates all points on the same line, or all lines through the same point.

isProjectivePlaneQuad :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph a projective plane with a quadrangle. This is a stronger non-degeneracy condition.

isGeneralizedQuadrangle :: Ord a => Hypergraph a -> Bool Source #

grid :: (Ord a, Ord b, Num a, Num b, Enum a, Enum b) => a -> b -> Hypergraph (a, b) Source #

dualGrid :: Integral a => a -> a -> Hypergraph a Source #

isGenQuadrangle' :: Ord a => Hypergraph a -> Bool Source #

isConfiguration :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph a (projective) configuration.

fanoPlane :: Hypergraph Integer Source #

heawoodGraph :: Graph (Either Integer [Integer]) Source #

The Heawood graph is the incidence graph of the Fano plane

desarguesConfiguration :: Hypergraph [Integer] Source #