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A cyclic permutation consisting of a single 8-cycle. There is not widespread consensus about the precise definition of a cyclic permutation. Some authors define a permutation σ of a set X to be cyclic if "successive application would take each object of the permuted set successively through the positions of all the other objects", [1] or, equivalently, if its representation in cycle notation ...
Circular shifts are used often in cryptography in order to permute bit sequences. Unfortunately, many programming languages, including C, do not have operators or standard functions for circular shifting, even though virtually all processors have bitwise operation instructions for it (e.g. Intel x86 has ROL and ROR).
An arrangement of distinct objects in a circular manner is called a circular permutation. [ 39 ] [ e ] These can be formally defined as equivalence classes of ordinary permutations of these objects, for the equivalence relation generated by moving the final element of the linear arrangement to its front.
1. Carmichael's definition of circular permutation (A permutation such as ... is called a circular permutation or a cyclic permutation. [and later] A circular permutation on two letters, such as (ab), is called a transposition. [and his first theorem is] Any given permutation is a product of circular permutations no two of which have a letter ...
The permutation by duplication mechanism for producing a circular permutation. First, a gene 1-2-3 is duplicated to form 1-2-3-1-2-3. Next, a start codon is introduced before the first domain 2 and a stop codon after the second domain 1, removing redundant sections and resulting in a circularly permuted gene 2-3-1.
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.
There are a few equivalent ways to state this definition. A cyclic order on X is the same as a permutation that makes all of X into a single cycle, which is a special type of permutation - a circular permutation. Alternatively, a cycle with n elements is also a Z n-torsor: a set with a free transitive action by a finite cyclic group. [1]
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