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On compositions of natural numbers (2007.06485v1)
Published 10 Jul 2020 in math.GM
Abstract: 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.