It refers to the different ways objects can be ordered or arranged, taking into account every possible order or sequence. Permutation is a mathematical concept that deals with the arrangement of objects in a specific order. Both permutation and combination play vital roles in various fields, including probability, statistics, and combinatorial analysis. It determines the number of ways objects can be chosen without repetition, where the order of selection does not matter. On the other hand, combination focuses on the selection of objects from a given set without considering their order. It calculates the number of ways objects can be arranged, taking into account all the different positions each object can occupy. Permutation refers to the arrangement of objects in a specific order, considering every possible order or sequence. In cryptography you might also encounter the term Pseudo Random Permutation (PRP), where "Permutation" basically just means a bijective function.To explain permutation and combination: Permutation and combination are mathematical concepts that deal with the arrangement and selection of elements. permutations don't necessarily have to have a set of string element indicies as their domain. It is however important to note that permutations don't have to be on the same form as $P$, i.e. Also, in some branches of mathematics, a permutation of an $n$-element set $S$ is commonly defined as a function from the set $\$.Ī note on terminology: Both the function $\sigma$ and the function $P$ above are permutations, since both are bijective functions. (In fact, some mathematicians prefer to reserve the word "permutation" only for the case where the domain is finite, and use the word "bijection" for the more general case described above others treat the two words as more or less synonymous. This is easy to see using a counting argument: since the number of possible inputs equals the number of possible outputs, if any two inputs are mapped to the same output, there must be at least one output which is left without any corresponding input, and vice versa.
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