Asymptotic normality of integer compositions inside a rectangle
  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 $\frac{ml}{2}$. 
Steffen Eger
math.CO cs.DM math.PR