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