In this paper we consider the absolute variation statistics of a composition σ = σ1 ··· σm of n which is a measure of the sum of absolute differences between each consecutive pair of parts in a composition. This and some related statistics which we d

The authors obtain precise asymptotic estimates for certain combinatorial sums over products of reciprocals of the summands in the partition or composition of a natural number n. These estimates are applied to determine the mean value of a certain arithmetical function over the polynomial ring $\mathbb{F}_q [ X ]$, where $\mathbb{F}_q $ is the finite field with q elements.