{"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/avoiding-abelian-and-additive-powers-in-rich","title":"Avoiding abelian and additive powers in rich words","arxiv_id":"2408.15390","date":"2024-08-27","proceeding":null,"authors":["Jonathan Andrade","Lucas Mol"],"abstract":"This paper concerns the avoidability of abelian and additive powers in infinite rich words. In particular, we construct an infinite additive $5$-power-free rich word over $\\{0,1\\}$ and an infinite additive $4$-power-free rich word over $\\{0, 1, 2\\}$. The alphabet sizes are as small as possible in both cases, even for abelian powers.","url_abs":"https://arxiv.org/abs/2408.15390v2","url_pdf":"https://arxiv.org/pdf/2408.15390v2.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":"avoiding-abelian-and-additive-powers-in-rich","repo_url":"https://github.com/lgmol/Additive-Powers-Decision-Algorithm","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}