Permutations

thumb|120 px|According to the first meaning of permutation, each of the six rows is a different permutation of three distinct balls|alt=The six different possible ways to order three balls of different colors: (red, green, blue), (red, blue, green), (green, red, blue), (green, blue, red), (blue, red, green), and (blue, green, red). In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or process of changing the linear order of an ordered set.

number game with 15 pieces but 16 spaces

matrices representing permutation of vector elements; with exactly one 1 per row and column

antisymmetric permutation object acting on tensors

method of encryption by which the positions held by units of plaintext (which are commonly characters or groups of characters) are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext

thumb|305px|Number of possible permutations and derangements of elements. ( factorial) is the number of -permutations; ( subfactorial) is the number of derangements – -permutations where all of the elements change their initial places.

integer whose multiples are digit permutations

important functions in combinatorics

theorem in group theory

type of (mathematical) permutation with no fixed element

numbers that cannot be reasonably predicted

mathematical counting-out question

group homomorphism from the symmetric group over a finite set to the two-element group {±1}

cipher design construction

kth smallest value in a statistical sample

theorem

thumb|The distribution of permutations in a 3-symbol superpermutation In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. While trivial superpermutations can simply be made up of every permutation concatenated together, superpermutations can also be shorter (except for the trivial case of n = 1) because overlap is allowed. For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations.

polynomial of the elements of a matrix

number of ways to partition a set of n objects into k non-empty subsets

algorithm for generating a random permutation of a finite set

prime number that remains prime after any permutation of its digits

number of permutations of n elements with k disjoint cycles

mathematical problem

in discrete mathematics, a pair of positions in a sequence where two elements are out of sorted order

numbers giving a solution to several counting problems in combinatorics

Method of random selection

function which returns the largest least common multiple of any partition of its input

an algorithm that generates all permutations of a finite set

method of bit-shuffling used to diffuse bits across S-boxes

sequence where any order is equally likely

combinatorial algorithm

in mathematics, a permutation in which the positions of pairs of elements are switched with one another

art of ringing a set of bells in mathematical patterns

type of permutation studied in combinatorics

mathematical constant

generating polynomial of the number of ways to place k non-attacking rooks on a m×n chessboard

Statistical test

thumb|300px|The permutohedron of order 4

mathematical concept

Matrix with exactly one nonzero entry in each row and each column

systematic classification of 12 related enumerative problems concerning two finite sets

Sequence of integers

assignment problem in combinatorial mathematics

In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.

type of permutation in combinatorial mathematics