Asymptotic normality of integer compositions inside a rectangle

2012/03/03 by Steffen Eger, Eger, Steffen
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #cs.DM #math.CO #math.PR

paper · pdf · doi:10.48550/arxiv.1203.0690

7 pages, 6 figures

arxiv created 2012/03/03 · openalex publication_date 2012/03/03 · arxiv updated 2012/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 (ml)/(2).

Citations

• Integer compositions with part sizes not exceeding k

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