The number of ways to arrange seven objects in a row is . The arrangements are called permutations. Combinatorialists use two notational systems for permutations.[more]
The first notation has positions on top and numbers of the rearranged objects on the bottom. It can be read as a mapping of a finite set of numbers, where the numbers on top get mapped to those below.
The second notation applies that mapping repeatedly to any starting number until there is a repetition. Then a new number is chosen to start the next cycle, and so on. A permutation can be shown as a directed graph.[less]