The notion "cyclic permutation" is used in different, but related ways:
- the elements of S may be ordered (c < c < ... < c[k]) and the mapping of P may be written as:
- p(c[i] ) = c[i + t] for i = 1, 2, ..., k − t, and
- p(c[i]) = c[i + t − k] for i = k − t + 1, k − t + 2, ..., k.
Cyclic permutations of definition type 1 are also called rotations, or circular shifts.
is a cyclic permutation with offset 2. It may be constructed with gcd(8, 2) = 2 cycles; see image. The used order is: c := 7, c :=6, c[i] = i else.
A permutation is called a cyclic permutation if and only if it will be constructed with exactly 1 cycle.
Note: Every permutation over a set with k elements is a cyclic permutation of definition type 2 if and only if it is a cyclic permutation of definition type 1 with gcd(k, offset) = 1
A permutation is called a cyclic permutation if and only if only one of the constructing cycles will have length > 1.
Note: Every cyclic permutation of definition type 3 may be seen as an union of a cyclic permutation of definition type 2 and some fixed points.
Every cyclic permutation of definition type 2 may be seen ″as a cyclic permutation of definition type 3 with zero fixed points.
Wikimedia Foundation. 2010.
Look at other dictionaries:
cyclic permutation — noun : a permutation in which a set of symbols is rearranged by putting the first for the last (as in ABC, BCA, CAB, ABC) or vice versa … Useful english dictionary
Cyclic order — In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order cannot be modeled as a binary relation a < b . One does not say that east is more clockwise than west.… … Wikipedia
Permutation — For other uses, see Permutation (disambiguation). The 6 permutations of 3 balls In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values.… … Wikipedia
Cyclic number — This article is about numbers where permutations of their digits (in some base) yield related numbers. For the number theoretic concept, see cyclic number (group theory). A summary of this article appears in Repeating decimal. A cyclic number is… … Wikipedia
Cyclic (mathematics) — There are many terms in mathematics that begin with cyclic: Cyclic chain rule, for derivatives, used in thermodynamics Cyclic code, linear codes closed under cyclic permutations Cyclic convolution, a method of combining periodic functions Cycle… … Wikipedia
Permutation group — In 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 (which are thought of as bijective functions from the set M to itself); the… … Wikipedia
List of permutation topics — This is a list of topics on mathematical permutations.*Alternating group *Alternating permutation *Bijection *Circular shift *Combination *Cycle index *Cycle notation *Cyclic order *Cyclic permutation *Derangement *Even and odd permutations… … Wikipedia
Transposable integer — A summary of this article appears in Repeating decimal. The digits of some specific integers permute or shift cyclically when they are multiplied by a number n. Examples are: 142857 × 3 = 428571 (shifts cyclically one place left) 142857 × 5 =… … Wikipedia
Fisher-Yates shuffle — The Fisher Yates shuffle, named after Ronald Fisher and Frank Yates, also known as the Knuth shuffle, after Donald Knuth, is an algorithm for generating a random permutation of a finite set in plain terms, for randomly shuffling the set. A… … Wikipedia
142857 (number) — 142,857 is the best known cyclic number in base 10. [ [http://www.daviddarling.info/encyclopedia/C/cyclic number.html Cyclic number ] , The Internet Encyclopedia of Science ] [Michael W. Ecker, [http://links.jstor.org/sici?sici=0049… … Wikipedia