title: List of permutation topics
text: # 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
  