List of permutation topics

Particular kinds of permutations

Alternating permutation

Circular shift

Cyclic permutation

Derangement

Even and odd permutations—see Parity of a permutation

Josephus permutation

Parity of a permutation

Separable permutation

Stirling permutation

Superpattern

Transposition (mathematics)

Unpredictable permutation

Combinatorics of permutations

Bijection

Combination

Costas array

Cycle index

Cycle notation

Cycles and fixed points

Cyclic order

Direct sum of permutations

Enumerations of specific permutation classes

Factorial

Falling factorial

Permutation matrix

Generalized permutation matrix

Inversion (discrete mathematics)

Major index

Ménage problem

Permutation graph

Permutation pattern

Permutation polynomial

Permutohedron

Rencontres numbers

Robinson–Schensted correspondence

Skew sum of permutations

Sum of permutations:

Direct sum of permutations

Skew sum of permutations

Stanley–Wilf conjecture

Symmetric function

Szymanski's conjecture

Twelvefold way

Groups

Alternating group

Automorphisms of the symmetric and alternating groups

Block (permutation group theory)

Cayley's theorem

Cycle index

Frobenius group

Galois group of a polynomial

Jucys–Murphy element

Landau's function

Oligomorphic group

O'Nan–Scott theorem

Parker vector

Permutation group

Place-permutation action

Primitive permutation group

Rank 3 permutation group

Representation theory of the symmetric group

Schreier vector

Strong generating set

Symmetric group

Symmetric inverse semigroup

Weak order of permutations

Wreath product

Young symmetrizer

Zassenhaus group

Zolotarev's lemma

Other algebraic structures

Burnside ring

Mathematics applicable to physical sciences

Antisymmetrizer

Identical particles

Levi-Civita symbol

Number theory

Permutable prime

Algorithms and information processing

Bit-reversal permutation

Claw-free permutation

Heap's algorithm

Permutation automaton

Schreier vector

Sorting algorithm

Sorting network

Substitution-permutation network

Steinhaus–Johnson–Trotter algorithm

Tompkins–Paige algorithm

Cryptography

Permutation box

Permutation cipher

Substitution cipher

Transposition cipher

Probability, stochastic processes, and statistics

Ewens' sampling formula

Fisher–Yates shuffle

Order statistic

Permutational analysis of variance

Rankit

Resampling (statistics)

Random permutations

Golomb–Dickman constant

Random permutation

Random permutation statistics

Music

Change ringing

Method ringing

Permutation (music)

Games

Faro shuffle

Fifteen puzzle

Shuffling