Expected number of distinct part sizes in a random integer composition (Q2711617)

For a positive integer \(n\), let \(D_n(\kappa)\) denote the number of distinct part sizes in a random composition \(\kappa\) of \(n\) (with respect to the uniform probability measure). In the paper under review the authors obtain an asymptotic expression (viz. \(\log_2n\) plus a constant plus a small but periodic oscillation) for the expectation of \(D_n\) as \(n\to \infty\). As they mention in a note added in proof, the same result has been obtained independently and by an entirely different method by \textit{H.-K. Hwang} and \textit{Y.-N. Yeh} [Adv. Appl. Math. 19, 378-414 (1997; Zbl 0943.05009)].