![]() Permutations differ from combinations, which are selections of some members of a set regardless of order. With a permutation, the order of numbers matters. ![]() 190x190px A permutation is called a cyclic permutation if and only if it has a single nontrivial cycle (a cycle of length > 1). The word "permutation" also refers to the act or process of changing the linear order of an ordered set. A permutation is the number of ways a set can be arranged or the number of ways things can be arranged. thumbupright1.7Diagram of a cyclic permutation with two fixed points a 6-cycle and two 1-cycles. the transfer of a segment of DNA from one site to another in the genome. This is a simple example of permutations. The number of different 4-digit-PIN which can be formed using these 10 numbers is 5040. In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. transposition: noun an act, process, or instance of transposing or being transposed. A permutation is an arrangement in a definite order of a number of objects taken some or all at a time. There is a similar rotation group with n elements for any regular n -gon. We call the group of permutations corresponding to rotations of the square the rotation group of the square. ![]() Mathematical version of an order change Each of the six rows is a different permutation of three distinct balls A set of permutations with these three properties is called a permutation group2 or a group of permutations. ![]()
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