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arXiv · 1203.2374

Part-products of $S$-restricted integer compositions

Eric Schmutz·Caroline Shapcott
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Abstract

If $S$ is a cofinite set of positive integers, an "$S$-restricted composition of $n$" is a sequence of elements of $S$, denoted $\vecλ=(λ_1,λ_2,...)$, whose sum is $n$. For uniform random $S$-restricted compositions, the random variable ${\bf B}(\vecλ)=\prod_i λ_i$ is asymptotically lognormal. The proof is based upon a combinatorial technique for decomposing a composition into a sequence of smaller compositions.

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Eric Schmutz, Caroline Shapcott. 2012-03-11. Part-products of $S$-restricted integer compositions. https://arxiv.org/abs/1203.2374

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