List of permutation topics
# List of permutation topics

This is a list of topics on mathematical permutations.

## 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
* 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
* 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
