{"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/repetitions-in-infinite-palindrome-rich-words","title":"Repetitions in infinite palindrome-rich words","arxiv_id":"1904.10028","date":"2019-04-22","proceeding":null,"authors":["Aseem Raj Baranwal","Jeffrey Shallit"],"abstract":"Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting open problems. We address lower bounds on the repetition threshold of infinite rich words over 2 and 3-letter alphabets, and construct a candidate infinite rich word over the alphabet $\\Sigma_2=\\{0,1\\}$ with a small critical exponent of $2+\\sqrt{2}/2$. This represents the first progress on an open problem of Vesti from 2017.","url_abs":"http://arxiv.org/abs/1904.10028v1","url_pdf":"http://arxiv.org/pdf/1904.10028v1.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":"repetitions-in-infinite-palindrome-rich-words","repo_url":"https://github.com/aseemrb/Walnut","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}