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...

mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G...

cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has...

the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations. If...

A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more...

entries 0.: 26  An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM...

Permutation City is a 1994 science-fiction novel by Greg Egan that explores many concepts, including quantum ontology, through various philosophical aspects...

A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a set...

Look up permutation in Wiktionary, the free dictionary. In mathematics, permutation relates to the act of arranging all the members of a set into some...

mathematical permutations. Alternating permutation Circular shift Cyclic permutation Derangement Even and odd permutations—see Parity of a permutation Josephus...

In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S is a bijection between two specified subsets of...

mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly...

The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms...

theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation...

permutations and permutation patterns, a permutation class is a set C {\displaystyle C} of permutations for which every pattern within a permutation in...

In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g...

cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with...

G} as a group of permutations, or as a group of permutation matrices. The term also refers to the combination of the two. A permutation representation of...

Combinations and permutations in the mathematical sense are described in several articles. Described together, in-depth: Twelvefold way Explained separately...

mathematical field of graph theory, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent pairs...

In applied mathematics, a bit-reversal permutation is a permutation of a sequence of n {\displaystyle n} items, where n = 2 k {\displaystyle n=2^{k}} is...

until no elements remain. The algorithm produces an unbiased permutation: every permutation is equally likely. The modern version of the algorithm takes...

epsilon represents a collection of numbers defined from the sign of a permutation of the natural numbers 1, 2, ..., n, for some positive integer n. It...

mathematics, a vexillary permutation is a permutation μ of the positive integers containing no subpermutation isomorphic to the permutation (2143); in other words...

In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters...

mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm...

combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set {1, 2, 3, ..., n} is a permutation (arrangement) of those numbers so...

separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations may be characterized...

that are out of their natural order. Let π {\displaystyle \pi } be a permutation. There is an inversion of π {\displaystyle \pi } between i {\displaystyle...

which is structured in such a way that information about how a group of permutations acts on a set can be simply read off from the coefficients and exponents...