The number of permutations with a given signature, and the expectations of their elements

This paper presents a new derivation of an enumeration formula for permutations of a given signature. Unlike the previous papers I use random number sequences which mimic the permutation, in the sense that they rise and fall as determined by the permutationʹs signature. Explicit expressions, previously unknown, are also derived for the mean values of the permutationʹs elements.