2020/07/10 by Douglas E. Iannucci, Iannucci, Douglas E.
Computer Science · Mathematics · #05-01 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #General Mathematics (math.GM) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2007.06485
openalex publication_date 2020/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this expository note, we introduce the reader to compositions of a natural number, e.g., 2+1+2+1+7+1 is a composition of 14, and 1+2 and 2+1 are two different compositions of 3. We discuss some simple restricted forms of compositions, e.g., 23+17+33 is a composition of 73 into three odd parts. We derive formulas that count the number of so restricted forms of compositions of a natural number n, and we conclude with a brief general discussion of the topic.