Part-Products of 1-Free Integer Compositions

Abstract

If $\vec{\lambda}$ is a composition of the positive integer $n$, define ${\bf B}(\vec{\lambda})$ to be the product of the parts of $\vec{\lambda}$. We present a modified version of Hitczenko's stopped sequence construction that leads to a proof of the asymptotic lognormality of ${\bf B}$ for random 1-free compositions (compositions containing no parts of size 1).