A note on the distribution of the different orderings of n objects

Abstract

Suppose that we have n objects, which may conveniently be represented by the integers 1, 2, 3, …, n. The total number of ways in which they can be ordered is n!. Let the order 1, 2, 3, …, n, be termed the normal order. Any other order can be classified according to the minimum number of interchanges (of one number with an adjacent one) required to restore the normal order.