%0 Journal Article
%T Part-products of $S$-restricted integer compositions
%A Eric Schmutz
%A Caroline Shapcott
%J Mathematics
%D 2012
%I arXiv
%X If $S$ is a cofinite set of positive integers, an "$S$-restricted composition of $n$" is a sequence of elements of $S$, denoted $\vec{\lambda}=(\lambda_1,\lambda_2,...)$, whose sum is $n$. For uniform random $S$-restricted compositions, the random variable ${\bf B}(\vec{\lambda})=\prod_i \lambda_i$ is asymptotically lognormal. The proof is based upon a combinatorial technique for decomposing a composition into a sequence of smaller compositions.
%U http://arxiv.org/abs/1203.2374v1