Asymptotic normality of integer compositions inside a rectangle

Abstract

Among all restricted integer compositions with at most $m$ parts, each of which has size at most $l$, choose one uniformly at random. Which integer does this composition represent? In the current note, we show that underlying distribution is, for large $m$ and $l$, approximately normal with mean value $\frac{ml}{2}$.

7 pages, 6 figures