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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 ...
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.
This would have been the first attempt on record to solve a difficult problem in permutations and combinations. [4] Al-Khalil (717–786), an Arab mathematician and cryptographer, wrote the Book of Cryptographic Messages. It contains the first use of permutations and combinations, to list all possible Arabic words with and without vowels. [5]
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.
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.
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 twelve problems of counting equivalence classes of functions do not involve the same difficulties, and there is not one systematic method for solving them. Two of the problems are trivial (the number of equivalence classes is 0 or 1), five problems have an answer in terms of a multiplicative formula of n and x, and the remaining five ...
Skew and direct sums of permutations; Steinhaus–Johnson–Trotter algorithm; Stirling number; Stirling numbers of the first kind; Stirling numbers of the second kind; Stirling permutation; Substitution–permutation network; Superpermutation