Part-products of S-restricted integer compositions

2012/03/11 by Eric Schmutz, Schmutz, Eric, Caroline Shapcott +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1203.2374

18 pages

arxiv created 2012/03/11 · arxiv updated 2012/03/13

Abstract

If S is a cofinite set of positive integers, an "S-restricted composition of n" is a sequence of elements of S, denoted λ=(λ₁,λ₂,...), whose sum is n. For uniform random S-restricted compositions, the random variable \bf B(λ)=∏_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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