On Powers of Some Power Series

2010/11/02 by Milan Janjić, Milan Janjic, Janjic, Milan
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #math.CO

paper · pdf · doi:10.48550/arxiv.1011.0525

arxiv created 2010/11/02 · openalex publication_date 2010/11/02 · arxiv updated 2010/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized compositions with a fixed number of parts are derived. Some results on compositions obtained in some recent papers are consequences of these formulas.

Citations

• Generalized Compositions of Natural Numbers

Related

• Power sums over commutative and unitary rings
• Conjectures involving a generalization of the sums of powers of integers
• On identities generated by compositions of positive integers
• On Number of Compositions of Natural Numbers
• A Formalization of Divided Powers in Lean