R: The Symmetric Group: Permutations of a Finite Set

# The Symmetric Group: Permutations of a Finite Set

## Documentation for package ‘permutations’ version 1.1-9-1

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

A C D E F G H I J K 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 with given characteristics
allcycles | All permutations with given characteristics
allcycn | All permutations with given characteristics
allperms | All permutations with given characteristics
allpermslike | All permutations with given characteristics
all_cyclic_shuffles | All permutations with given characteristics
all_perms_shape | All permutations with given characteristics
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 | Coerce a permutation to a function
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
caydist | Cayley distance
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: the dot object
conjugate | Are two permutations conjugate?
conjugation | Arithmetic Ops Group Methods for permutations
cycle | Functions to create and coerce word objects and cycle objects
cycle2word | Functions to create and coerce word objects and cycle objects
cycletype | Shape of a permutation
cycle_plus_integer_elementwise | Arithmetic Ops Group Methods for permutations
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
cycle_type | Shape of a permutation
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
doesnotmove | Stabilizer of a permutation
dot | Group-theoretic commutator: the dot object
dot-class | Group-theoretic commutator: the dot object
dot_error | Group-theoretic commutator: the dot object
DY | megaminx

## -- E --

edge_facets | The Megaminx Superflip
Extract | Extract or Replace elements of permutation vectors
extract | Group-theoretic commutator: 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
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.flip | The Megaminx Superflip
is.flip_pair | The Megaminx Superflip
is.flip_singleperm | The Megaminx Superflip
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.stabilizer | Stabilizer of a permutation
is.superflip | The Megaminx Superflip
is.word | Functions to create and coerce word objects and cycle objects

## -- J --

jacobi | Group-theoretic commutator: the dot object

## -- K --

keepcyc | Keep or discard some cycles of a permutation

## -- 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_superflip | The Megaminx Superflip
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.
ncyc | Cayley distance
nfixed | Cayley distance
nicify | details of cyclists
nicify_cyclist | details of cyclists
nmoved | Cayley distance
nullcycle | Null permutations
nullperm | Null permutations
nullword | Null permutations

## -- O --

O | megaminx
oneline | Print methods for permutation objects
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
outer | Outer product of vectors of permutations
outer-method | Outer product of vectors of permutations
outer.cycle | Outer product of vectors of permutations
outer.permutation | Outer product of vectors of permutations
outer.word | Outer product of vectors of permutations

## -- 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: 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_oneline | Print methods for permutation objects
print_word | Print methods for permutation objects
print_word_as_cycle | 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
Replace | Extract or Replace elements of permutation vectors
rgivenshape | Random permutations
rgs1 | Random permutations
riffle | Faro shuffles
rperm | Random permutations
rpermm | 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
some_perms_shape | All permutations with given characteristics
stabilized | Stabilizer of a permutation
stabilizer | Stabilizer of a permutation
stabilizes | Stabilizer of a permutation
standard | The fundamental bijection
standard_cyclist | The fundamental bijection
sum.cycle | Arithmetic Ops Group Methods for permutations
sum.permutation | Arithmetic Ops Group Methods for permutations
sum1 | Arithmetic Ops Group Methods for permutations
sum_permutation_single | Arithmetic Ops Group Methods for permutations
superflip | The Megaminx Superflip
swap | Length-2 cycles; swap a pair of elements

## -- 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: the dot object
[-method | Group-theoretic commutator: the dot object
[.cycle | Extract or Replace elements of permutation vectors
[.dot | Group-theoretic commutator: the dot object
[.permutation | Extract or Replace elements of permutation vectors
[.word | Extract or Replace elements of permutation vectors
[<- | Extract or Replace elements of permutation vectors
[<-.cycle | Extract or Replace elements of permutation vectors
[<-.permutation | Extract or Replace elements of permutation vectors
[<-.word | Extract or Replace elements of permutation vectors