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
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