{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/asymptotic-analysis-of-compositions-using","title":"On the Enumeration and Asymptotic Analysis of Fibonacci Compositions","arxiv_id":"2110.14478","date":"2021-10-27","proceeding":null,"authors":["Joshua M. Siktar"],"abstract":"We study Fibonacci compositions, which are compositions of natural numbers that only use Fibonacci numbers, in two different contexts. We first prove inequalities comparing the number of Fibonacci compositions to regular compositions where summands have a maximum possible value. Then, we consider asymptotic properties of Fibonacci compositions, comparing them to compositions whose terms come from positive linear recurrence sequences. Finally, we consider analogues of these results where we do not allow the use of a certain number of consecutive Fibonacci numbers starting from $F_2 = 1$.","url_abs":"https://arxiv.org/abs/2110.14478v3","url_pdf":"https://arxiv.org/pdf/2110.14478v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"asymptotic-analysis-of-compositions-using","repo_url":"https://github.com/jmsiktar/fibbins","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}