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 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