On compositions of natural numbers
Douglas E. Iannucci

TL;DR
This paper introduces compositions of natural numbers, explores restricted forms such as odd parts, derives counting formulas for these forms, and discusses their properties in an expository manner.
Contribution
It provides formulas for counting restricted compositions of natural numbers, focusing on specific forms like odd parts, and offers an accessible overview of the topic.
Findings
Derived formulas for counting compositions with restrictions
Analyzed compositions with odd parts and other simple restrictions
Provided an expository discussion on compositions of natural numbers
Abstract
In this expository note, we introduce the reader to compositions of a natural number, e.g., is a composition of 14, and and are two different compositions of 3. We discuss some simple restricted forms of compositions, e.g., 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 , and we conclude with a brief general discussion of the topic.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · semigroups and automata theory · Advanced Mathematical Identities
