generating permutation
1Permutation — For other uses, see Permutation (disambiguation). The 6 permutations of 3 balls In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values.… …
2Permutation group — In mathematics, a permutation group is a group G whose elements are permutations of a given set M , and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself); the… …
3Generating function — This article is about generating functions in mathematics. For generating functions in classical mechanics, see Generating function (physics). For signalling molecule, see Epidermal growth factor. In mathematics, a generating function is a formal …
4Random permutation statistics — The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example,… …
5Stirling numbers and exponential generating functions — The use of exponential generating functions or EGFs to study the properties of Stirling numbers is a classical exercise in combinatorics and possibly the canonical example of how symbolic combinatorics, the method that encapsulates the… …
6Random permutation — A random permutation is a random ordering of a set of objects, that is, a permutation valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms. Such fields include coding theory,… …
7Examples of generating functions — The following examples are in the spirit of George Pólya, who advocated learning mathematics by doing and re capitulating as many examples and proofs as possible. The purpose of this article is to present common tricks of the trade in context, so …
8Strong generating set — Let G leq S n be a permutation group. Let : B = (eta 1, eta 2, ldots, eta r) be a sequence of distinct integers, eta i in { 1, 2, ldots, n } , such that the pointwise stabilizer of B is trivial (ie: let B be a base for G ). Define : B i =… …
9Alternating permutation — In combinatorial mathematics, an alternating permutation of the set {1, 2, 3, ..., n } is an arrangement of those numbers into an order c 1, ..., c n such that no element c i is between c i − 1 and c i + 1 for any value of i and c 1 lt; c 2.Let A …
10Fisher-Yates shuffle — The Fisher Yates shuffle, named after Ronald Fisher and Frank Yates, also known as the Knuth shuffle, after Donald Knuth, is an algorithm for generating a random permutation of a finite set in plain terms, for randomly shuffling the set. A… …
