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- Permutation abstract "In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). These are all the possible orderings of this three element set. As another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. In this example, the letters are already ordered in the original word and the anagram is a reordering of the letters. The study of permutations of finite sets is a topic in the field of combinatorics.Permutations occur, in more or less prominent ways, in almost every area of mathematics. They often arise when different orderings on certain finite sets are considered, possibly only because one wants to ignore such orderings and needs to know how many configurations are thus identified. For similar reasons permutations arise in the study of sorting algorithms in computer science.The number of permutations of n distinct objects is n factorial usually written as n!, which means the product of all positive integers less than or equal to n.In algebra and particularly in group theory, a permutation of a set S is defined as a bijection from S to itself. That is, it is a function from S to S for which every element occurs exactly once as an image value. This is related to the rearrangement of the elements of S in which each element s is replaced by the corresponding f(s). The collection of such permutations form a group called the symmetric group of S. The key to this group's structure is the fact that the composition of two permutations (performing two given rearrangements in succession) results in another rearrangement. Permutations may act on structured objects by rearranging their components, or by certain replacements (substitutions) of symbols.In elementary combinatorics, the k-permutations, or partial permutations, are the ordered arrangements of k distinct elements selected from a set. When k is equal to the size of the set, these are the permutations of the set.".
- Permutation thumbnail Permutations_RGB.svg?width=300.
- Permutation wikiPageExternalLink 1000px-Symmetric_group_4%3B_permutation_list_with_matrices.svg.png.
- Permutation wikiPageID "44027".
- Permutation wikiPageLength "71124".
- Permutation wikiPageOutDegree "169".
- Permutation wikiPageRevisionID "678301309".
- Permutation wikiPageWikiLink 3GPP_Long_Term_Evolution.
- Permutation wikiPageWikiLink Adjacent_transposition.
- Permutation wikiPageWikiLink Algebra.
- Permutation wikiPageWikiLink Alternating_permutation.
- Permutation wikiPageWikiLink Anagram.
- Permutation wikiPageWikiLink Ancient_Society_of_College_Youths.
- Permutation wikiPageWikiLink Array_data_structure.
- Permutation wikiPageWikiLink Associative.
- Permutation wikiPageWikiLink Associative_property.
- Permutation wikiPageWikiLink Augustin-Louis_Cauchy.
- Permutation wikiPageWikiLink Bhāskara_II.
- Permutation wikiPageWikiLink Big_O_notation.
- Permutation wikiPageWikiLink Bijection.
- Permutation wikiPageWikiLink Bijections.
- Permutation wikiPageWikiLink Bijective.
- Permutation wikiPageWikiLink Binomial_coefficient.
- Permutation wikiPageWikiLink Bubble_sort.
- Permutation wikiPageWikiLink Cardinality.
- Permutation wikiPageWikiLink Category:Factorial_and_binomial_topics.
- Permutation wikiPageWikiLink Category:Permutations.
- Permutation wikiPageWikiLink Cayley_table.
- Permutation wikiPageWikiLink Cayleys_theorem.
- Permutation wikiPageWikiLink Change_of_variables.
- Permutation wikiPageWikiLink Change_ringing.
- Permutation wikiPageWikiLink Combination.
- Permutation wikiPageWikiLink Combinatorics.
- Permutation wikiPageWikiLink Commutative_property.
- Permutation wikiPageWikiLink Composition_(mathematics).
- Permutation wikiPageWikiLink Composition_of_functions.
- Permutation wikiPageWikiLink Computer_science.
- Permutation wikiPageWikiLink Conjugacy_class.
- Permutation wikiPageWikiLink Convolution.
- Permutation wikiPageWikiLink Cycle_index.
- Permutation wikiPageWikiLink Cycle_type.
- Permutation wikiPageWikiLink Cyclic_order.
- Permutation wikiPageWikiLink Cyclic_permutation.
- Permutation wikiPageWikiLink Derangement.
- Permutation wikiPageWikiLink Disjoint_sets.
- Permutation wikiPageWikiLink Dominique_Foata.
- Permutation wikiPageWikiLink Donald_Knuth.
- Permutation wikiPageWikiLink Error_detection_and_correction.
- Permutation wikiPageWikiLink Eulerian_number.
- Permutation wikiPageWikiLink Even_and_odd_permutations.
- Permutation wikiPageWikiLink Fabian_Stedman.
- Permutation wikiPageWikiLink Factorial.
- Permutation wikiPageWikiLink Factorial_number_system.
- Permutation wikiPageWikiLink Finite_set.
- Permutation wikiPageWikiLink Fixed_point_(mathematics).
- Permutation wikiPageWikiLink Forward_error_correction.
- Permutation wikiPageWikiLink Frank_Yates.
- Permutation wikiPageWikiLink Function_(mathematics).
- Permutation wikiPageWikiLink Function_composition.
- Permutation wikiPageWikiLink Galois_theory.
- Permutation wikiPageWikiLink Group_(mathematics).
- Permutation wikiPageWikiLink Group_action.
- Permutation wikiPageWikiLink Group_representation.
- Permutation wikiPageWikiLink Group_theory.
- Permutation wikiPageWikiLink Heaps_algorithm.
- Permutation wikiPageWikiLink Heinrich_August_Rothe.
- Permutation wikiPageWikiLink Identity_function.
- Permutation wikiPageWikiLink Identity_permutation.
- Permutation wikiPageWikiLink Image_(mathematics).
- Permutation wikiPageWikiLink Increasing.
- Permutation wikiPageWikiLink Induction_(mathematics).
- Permutation wikiPageWikiLink Insertion_sort.
- Permutation wikiPageWikiLink Interleaver.
- Permutation wikiPageWikiLink Inverse_function.
- Permutation wikiPageWikiLink Inversion_(discrete_mathematics).
- Permutation wikiPageWikiLink Isomorphism.
- Permutation wikiPageWikiLink Joseph-Louis_Lagrange.
- Permutation wikiPageWikiLink Joseph_Louis_Lagrange.
- Permutation wikiPageWikiLink Josephus_permutation.
- Permutation wikiPageWikiLink Josephus_problem.
- Permutation wikiPageWikiLink LTE_(telecommunication).
- Permutation wikiPageWikiLink Lehmer_code.
- Permutation wikiPageWikiLink Levi-Civita_symbol.
- Permutation wikiPageWikiLink Lexicographic_order.
- Permutation wikiPageWikiLink Lexicographic_ordering.
- Permutation wikiPageWikiLink Lexicographical_order.
- Permutation wikiPageWikiLink Lilavati.
- Permutation wikiPageWikiLink Linked_list.
- Permutation wikiPageWikiLink List_of_order_structures_in_mathematics.
- Permutation wikiPageWikiLink List_of_permutation_topics.
- Permutation wikiPageWikiLink Līlāvatī.
- Permutation wikiPageWikiLink Major_index.
- Permutation wikiPageWikiLink Mathematical_induction.
- Permutation wikiPageWikiLink Mathematics.
- Permutation wikiPageWikiLink Matrix_(mathematics).
- Permutation wikiPageWikiLink Meander_(mathematics).
- Permutation wikiPageWikiLink Miklós_Bóna.
- Permutation wikiPageWikiLink Mixed_radix.
- Permutation wikiPageWikiLink Monotonic_function.
- Permutation wikiPageWikiLink Multinomial_coefficient.