repthy
Class S_n

Object
  AbstractCollection
      AbstractSet
          ImmutableSet
              Group
                  HashGroup
                      PermGp
                          S_n

All Implemented Interfaces:

Collection, Set

public class S_n

extends PermGp

The group S_n consisting of all permutations of the integers 0, ..., n-1. The degree is the obvious value n.

Author:

Mark McConnell

Field Summary

Fields inherited from class Group

charTable

Constructor Summary

S_n(int n)
Constructor.

Method Summary

protected void	fillInCharTable() The tables for S1 through S5 are hard-coded; the rest are computed by the super method.
CharTable	getCharTable() Same as the regular method, except uses the theorem that every value in the character table is an integer if (and only if) the group is Sn.
int	getDegree() Returns the common degree of the PermGpElts that make up the group.
Subgroup	getStabilizer(int i) Returns the subgroup consisting of elements that fix i.
boolean	isSimple() Whether this group is simple.
static void	main(String[] args) For testing.
String	toString()

Methods inherited from class HashGroup

contains, getConjClass, getConjClassIndex, getConjClassNum, iterator, size

Methods inherited from class Group

cyclicSubgpsUpToConj, describeOrder8, elementarySubgps, getCenter, getCentralizer, getCharComparator, getCommutatorSubgroup, getCompositionSeries, getConjClassRep, getEltOrder, getEltOrder, getIdentity, getOrder, getProperNormalSubgroup, getSylow, isAbelian, isCentral, isSubgroupOf, order, power, printTest, tableTest

Methods inherited from class ImmutableSet

add, addAll, clear, remove, removeAll, retainAll

Methods inherited from class AbstractSet

equals, hashCode

Methods inherited from class AbstractCollection

containsAll, isEmpty, toArray, toArray

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface Set

containsAll, isEmpty, toArray, toArray

Constructor Detail

S_n

public S_n(int n)

Constructor.

Throws:

IllegalArgumentException - If n is less than 1.

Method Detail

getCharTable

public CharTable getCharTable()

Same as the regular method, except uses the theorem that every value in the character table is an integer if (and only if) the group is S_n.

Overrides:

getCharTable in class Group

fillInCharTable

protected void fillInCharTable()
                        throws OrthonormalityException,
                               PariNotFoundException

The tables for S₁ through S₅ are hard-coded; the rest are computed by the super method.

Overrides:

fillInCharTable in class Group

Throws:

OrthonormalityException - If the table isn't full at the end, or if anything goes wrong in the middle.

PariNotFoundException

getDegree

public int getDegree()

Description copied from class: PermGp

Returns the common degree of the PermGpElts that make up the group.

Overrides:

getDegree in class PermGp

getStabilizer

public Subgroup getStabilizer(int i)

Returns the subgroup consisting of elements that fix i.

Throws:

ArrayIndexOutOfBoundsException - if i is outside the range 0 leq i less than the degree.

isSimple

public boolean isSimple()

Description copied from class: Group

Whether this group is simple.

Overrides:

isSimple in class Group

toString

public String toString()

main

public static void main(String[] args)
                 throws OrthonormalityException

For testing. Takes one argument n.

Throws:

OrthonormalityException