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

Abstract

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 permutation's signature. Explicit expressions, previously unknown, are also derived for the mean values of the permutation's elements. © 2001 Elsevier Science B.V. All rights reserved.