A number system for the permutations

Abstract

A number system described here is particularly suitable for numbering the permutations. An algorithm is then presented by which the permutation associated with a number of this kind may be obtained. Since arithmetical operations, such as the addition of 1, are easily performed in the number system, one may make use of the algorithm to generate the permutations one at a time, using a minimal amount of work space. Employed for this purpose, it provides an alternative to the method given in [1].