This is a list of topics on mathematical permutations.

Particular kinds of permutations

• Alternating permutation

• Circular shift

• Cyclic permutation

• Derangement

• Even and odd permutationssee 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

Sum of permutations:

• Direct sum of permutations

• Skew sum of permutations

• Stanley–Wilf conjecture

• Symmetric function

• Szymanski's conjecture

• Twelvefold way

Permutation groups and other algebraic structures

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

Mathematical analysis

• Conditionally convergent series

Riemann series theorem

• Lévy–Steinitz theorem

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

• Substitution box

• Permutation cipher

• Substitution cipher

• Transposition cipher

Probability, stochastic processes, and statistics

• Combinatorial data analysis

• Ewens' sampling formula

• Fisher–Yates shuffle

• Order statistic

• Permutation test

• Permutational analysis of variance

• Rankit

• Resampling (statistics)

• Seriation (statistics)

Random permutations

• Golomb–Dickman constant

• Random permutation

• Random permutation statistics

Music

• Change ringing

• Method ringing

• Permutation (music)

Games

• Faro shuffle

• Fifteen puzzle

• Shuffling