Safe Haskell | None |
---|---|
Language | Haskell98 |
Math.Combinatorics.Hypergraph
Description
A module defining a type for hypergraphs.
- 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 :: (Num t, Eq a) => Hypergraph a -> [[t]]
- fromIncidenceMatrix :: (Ord a, Num a1, Num a, Eq a1, Enum a) => [[a1]] -> Hypergraph a
- 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 t1, Ord t, Num t1, Num t, Enum t1, Enum t) => t -> t1 -> Hypergraph (t, t1)
- 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 t => Hypergraph t -> Graph [t]
Documentation
data Hypergraph a Source #
Constructors
H [a] [[a]] |
Instances
Eq a => Eq (Hypergraph a) Source # | |
Ord a => Ord (Hypergraph a) Source # | |
Show a => Show (Hypergraph a) Source # | |
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
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 :: (Num t, Eq a) => Hypergraph a -> [[t]] Source #
fromIncidenceMatrix :: (Ord a, Num a1, Num a, Eq a1, Enum a) => [[a1]] -> Hypergraph a 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 #
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.
heawoodGraph :: Graph (Either Integer [Integer]) Source #
The Heawood graph is the incidence graph of the Fano plane
coxeterGraph :: Graph [Integer] Source #
tutteCoxeterGraph :: Graph (Either [Integer] [[Integer]]) Source #
The Tutte-Coxeter graph, also called the Tutte 8-cage
intersectionGraph :: Ord t => Hypergraph t -> Graph [t] Source #