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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).
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 ...
Every permutation on finitely many elements can be decomposed into cyclic permutations whose non-trivial orbits are disjoint. [5] The individual cyclic parts of a permutation are also called cycles, thus the second example is composed of a 3-cycle and a 1-cycle (or fixed point) and the third is composed of two 2-cycles.
For example, the permutation ... on record to solve a difficult problem in permutations and combinations. ... in a circular manner is called a circular permutation.
A circular order on the disjoint union L 1 ∪ L 2 ∪ {–∞, ∞} is defined by ∞ < L 1 < –∞ < L 2 < ∞, where the induced ordering on L 1 is the opposite of its original ordering. For example, the set of all longitudes is circularly ordered by joining all points west and all points east, along with the prime meridian and the 180th ...
In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games are used to pick out a person from a group, e.g. eeny, meeny, miny, moe. A drawing for the Josephus problem sequence for 500 people and skipping value of 6.
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive. The rules state that each prisoner may open only 50 drawers and cannot communicate with other prisoners.
A typical example is the permutation (1 3)(2)(4): it is a circular permutation for some authors; if the numbers represent the edges of a square, this permutation is the symmetry with respect to a diagonal, which is never considered, in geometry, as a cyclic permutation.