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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 ...
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.
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.
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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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 ...
Circular permutation in proteins; ... Skew and direct sums of permutations; ... Statistics; Cookie statement; Mobile view ...
The size n of the orbit is called the length of the corresponding cycle; when n = 1, the single element in the orbit is called a fixed point of the permutation. A permutation is determined by giving an expression for each of its cycles, and one notation for permutations consist of writing such expressions one after another in some order.