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Two examples of frequently used methods that have problems correctly aligning proteins related by circular permutation are dynamic programming and many hidden Markov models. [34] As an alternative to these, a number of algorithms are built on top of non-linear approaches and are able to detect topology -independent similarities, or employ ...
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 ...
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]
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 ...
The set X may represent a finite set of beads, and G may be a chosen group of permutations of the beads. For example, if X is a necklace of n beads in a circle, then rotational symmetry is relevant so G is the cyclic group C n, while if X is a bracelet of n beads in a circle, rotations and reflections are relevant so G is the dihedral group D n ...
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 ...
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).
Parity of a permutation; Permanent (mathematics) Permutable prime; Permutation (music) Permutation automaton; Permutation box; Permutation matrix; Permutation polynomial; Permutoassociahedron; Permutohedron; Place-permutation action; Plain hunt; Pseudorandom permutation