graph.symmetry

Class PermutationGroup

java.lang.Object

graph.symmetry.PermutationGroup

public class PermutationGroup
extends java.lang.Object

Represents a permutation group and contains methods for its analysis

Author:

Renata

Constructor Summary

Constructors

Constructor and Description
PermutationGroup(Permutation reflection, Permutation rotation) Constructs a permutation group given a reflection and/or a rotation

Method Summary

Modifier and Type	Method and Description
java.util.List<java.lang.Integer>	fix() Finds vertices fixed by the group
java.util.List<Permutation>	getPermutations()
boolean	isSemiRegular() Checks if the group is semi-regular Group is semi-regular if no permutation which is not an identity has fixed points
java.util.List<java.lang.Integer>	orbit(java.lang.Integer u) Finds an orbit of the group with resepct to a vertex
void	setPermutations(java.util.List<Permutation> permutations)
int	size()
java.util.List<Permutation>	stabilizers(java.lang.Integer u) Finds stabilizers of the group with respect to some vertex
java.util.List<Permutation>	subsetStabilizers(java.util.List<java.lang.Integer> Y) Finds stabilizers of the groups with respect to a subset of vertices
java.lang.String	toString()

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

PermutationGroup

public PermutationGroup(Permutation reflection,
                        Permutation rotation)

Constructs a permutation group given a reflection and/or a rotation

Parameters:

reflection - Reflection permutation. Can be null.

rotation - Rotation permutation Can be null.

Method Detail

stabilizers

public java.util.List<Permutation> stabilizers(java.lang.Integer u)

Finds stabilizers of the group with respect to some vertex

Parameters:

u - Vertex

Returns:

A list of all stabilizers with respect to some given u

subsetStabilizers

public java.util.List<Permutation> subsetStabilizers(java.util.List<java.lang.Integer> Y)

Finds stabilizers of the groups with respect to a subset of vertices

Parameters:

Y - Subset

Returns:

A list of stabilizers with respect to a subset Y

fix

public java.util.List<java.lang.Integer> fix()

Finds vertices fixed by the group

Returns:

A list of vertices fixed by the permutations

orbit

public java.util.List<java.lang.Integer> orbit(java.lang.Integer u)

Finds an orbit of the group with resepct to a vertex

Parameters:

u - Vertex

Returns:

An orbit (list of vertices) of the group with respect to u

isSemiRegular

public boolean isSemiRegular()

Checks if the group is semi-regular Group is semi-regular if no permutation which is not an identity has fixed points

Returns:

true if the group is semi-regular false otherwise

size

public int size()

Returns:

Size of the permutation group

getPermutations

public java.util.List<Permutation> getPermutations()

Returns:

Permutations forming the group

setPermutations

public void setPermutations(java.util.List<Permutation> permutations)

Parameters:

permutations - Permutations to set

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object