The Symmetric Group: Permutations of a Finite Set

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Documentation for package ‘permutations’ version 1.1-2

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A C D E F G H I J L M N O P R S T V W misc

permutations-package The Symmetric Group: Permutations of a Finite Set

-- A --

addcols Gets or sets the size of a permutation
allcyc All permutations of a given size and all cycles of a given length
allcycles All permutations of a given size and all cycles of a given length
allperms All permutations of a given size and all cycles of a given length
are_conjugate Are two permutations conjugate?
are_conjugate_single Are two permutations conjugate?
as.character.cycle Print methods for permutation objects
as.character_cyclist Print methods for permutation objects
as.cycle Functions to create and coerce word objects and cycle objects
as.function.cycle Coerce a permutation to a function
as.function.permutation Coerce a permutation to a function
as.function.word Coerce a permutation to a function
as.matrix Functions to create and coerce word objects and cycle objects
as.matrix.word Functions to create and coerce word objects and cycle objects
as.perm_matrix Permutation matrices
as.word Functions to create and coerce word objects and cycle objects

-- C --

c Concatenation of permutations
c.cycle Concatenation of permutations
c.word Concatenation of permutations
capply Apply functions to elements of a cycle
Cayley Cayley tables for permutation groups
cayley Cayley tables for permutation groups
ccps Arithmetic Ops Group Methods for permutations
char2cycle Functions to create and coerce word objects and cycle objects
char2cyclist_single details of cyclists
commutator Group-theoretic commutator and group action; the dot object
conjugate Are two permutations conjugate?
cycle Functions to create and coerce word objects and cycle objects
cycle2word Functions to create and coerce word objects and cycle objects
cycle_power Arithmetic Ops Group Methods for permutations
cycle_power_single Arithmetic Ops Group Methods for permutations
cycle_sum Arithmetic Ops Group Methods for permutations
cycle_sum_single Arithmetic Ops Group Methods for permutations
cyclist details of cyclists
cyclist2word_single details of cyclists
cyclist_valid Functions to validate permutations
cyc_len Functions to create and coerce word objects and cycle objects

-- D --

DB megaminx
derangement Tests for a permutation being a derangement
DG megaminx
dodecahedron The dodecahedron group
dodecahedron_edge The dodecahedron group
dodecahedron_face The dodecahedron group
dot Group-theoretic commutator and group action; the dot object
dot-class Group-theoretic commutator and group action; the dot object
dot_error Group-theoretic commutator and group action; the dot object
DY megaminx

-- E --

extract Group-theoretic commutator and group action; the dot object

-- F --

faro Faro shuffles
faro_gen Faro shuffles
fbin The fundamental bijection
fbin_inv The fundamental bijection
fbin_single The fundamental bijection
fixed Fixed elements
fixed.cycle Fixed elements
fixed.word Fixed elements
full_dodecahedron_edge The dodecahedron group
full_dodecahedron_face The dodecahedron group

-- G --

get1 Retrieve particular cycles or components of cycles
get_cyc Retrieve particular cycles or components of cycles
group_action Arithmetic Ops Group Methods for permutations
Gy megaminx

-- H --

helper Arithmetic Ops Group Methods for permutations

-- I --

id The identity permutation
inverse Inverse of a permutation
inverse.cycle Inverse of a permutation
inverse.word Inverse of a permutation
inverse_cyclist_single Inverse of a permutation
inverse_word_single Inverse of a permutation
is.cycle Functions to create and coerce word objects and cycle objects
is.derangement Tests for a permutation being a derangement
is.even Sign of a permutation
is.id The identity permutation
is.id.cycle The identity permutation
is.id.list The identity permutation
is.id.word The identity permutation
is.id_single_cycle The identity permutation
is.odd Sign of a permutation
is.permutation Functions to create and coerce word objects and cycle objects
is.perm_matrix Permutation matrices
is.word Functions to create and coerce word objects and cycle objects

-- J --

jacobi Group-theoretic commutator and group action; the dot object

-- L --

LB megaminx
length.permutation Various vector-like utilities for permutation objects.
length.word Various vector-like utilities for permutation objects.
length<-.permutation Various vector-like utilities for permutation objects.
LG megaminx
LY megaminx

-- M --

megaminx megaminx
megaminx_colours megaminx
megaminx_pentagons Plotting routine for megaminx sequences
megaminx_plotter Plotting routine for megaminx sequences
megaminx_quads Plotting routine for megaminx sequences
megaminx_triangles Plotting routine for megaminx sequences

-- N --

names Various vector-like utilities for permutation objects.
names.word Various vector-like utilities for permutation objects.
names<-.word Various vector-like utilities for permutation objects.
nicify details of cyclists
nicify_cyclist details of cyclists
nullcycle Null permutations
nullperm Null permutations
nullword Null permutations

-- O --

O megaminx
Ops Arithmetic Ops Group Methods for permutations
Ops.permutation Arithmetic Ops Group Methods for permutations
Ops.permutations Arithmetic Ops Group Methods for permutations
orbit Orbits of integers
orbit_single Orbits of integers

-- P --

padshape Shape of a permutation
permmatrix Permutation matrices
permorder The order of a permutation
permprod Arithmetic Ops Group Methods for permutations
permutation Functions to create and coerce word objects and cycle objects
permutation-class Group-theoretic commutator and group action; the dot object
permutations The Symmetric Group: Permutations of a Finite Set
permutation_matrix Permutation matrices
perm_matrix Permutation matrices
Pi megaminx
pm_to_perm Permutation matrices
print.cycle Print methods for permutation objects
print.permutation Print methods for permutation objects
print.word Print methods for permutation objects
print_cycle Print methods for permutation objects
print_word Print methods for permutation objects
Pu megaminx

-- R --

R megaminx
r1cyc Random permutations
rcyc Random permutations
rcycle Random permutations
remove_length_one details of cyclists
rep.permutation Concatenation of permutations
riffle Faro shuffles
rperm Random permutations
rword Random permutations

-- S --

sgn Sign of a permutation
shape Shape of a permutation
shapepart Shape of a permutation
shapepart_cyclist Shape of a permutation
shape_cyclist Shape of a permutation
shift_cycle Functions to create and coerce word objects and cycle objects
shuffle Faro shuffles
singleword_valid Functions to validate permutations
size Gets or sets the size of a permutation
size.cycle Gets or sets the size of a permutation
size.word Gets or sets the size of a permutation
size<- Gets or sets the size of a permutation
size<-.cycle Gets or sets the size of a permutation
size<-.word Gets or sets the size of a permutation
standard The fundamental bijection
standard_cyclist The fundamental bijection
superflip megaminx

-- T --

tidy Utilities to neaten permutation objects
trim Utilities to neaten permutation objects

-- V --

valid Functions to validate permutations
validity Functions to validate permutations
vec2cyclist_single details of cyclists
vec2cyclist_single_cpp details of cyclists
vps Arithmetic Ops Group Methods for permutations

-- W --

W megaminx
word Functions to create and coerce word objects and cycle objects
word_equal Arithmetic Ops Group Methods for permutations
word_prod Arithmetic Ops Group Methods for permutations
word_prod_single Arithmetic Ops Group Methods for permutations

-- misc --

%~% Are two permutations conjugate?
%~%.permutation Are two permutations conjugate?
. Group-theoretic commutator and group action; the dot object
[-method Group-theoretic commutator and group action; the dot object
[.dot Group-theoretic commutator and group action; the dot object