{"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/centralizers-in-the-plactic-monoid","title":"Centralizers in the plactic monoid","arxiv_id":"2410.20460","date":"2024-10-27","proceeding":null,"authors":["Bruce E. Sagan","Alexander N. Wilson"],"abstract":"Let u be a word over the positive integers. Motivated in part by a question from representation theory, we study the centralizer set of u which is C(u) = {w | uw is Knuth-equivalent to wu}. In particular, we give various necessary conditions for w to be in C(u). We also characterize C(u) when u has few letters, when it has a single repeated entry, or when it is a certain type of decreasing sequence. We consider c_{n,m}(u), the number of w in C(u) of length n with max w at most m. We prove that for |u| = 1 the value of this function depends only on the relative sizes of u and m and not on their actual values. And for various u we use Stanley's theory of poset partitions to show that, for fixed n, c_{n,m}(u) is a polynomial in m with certain degree and leading coefficient. We end with various conjectures and directions for further research.","url_abs":"https://arxiv.org/abs/2410.20460v1","url_pdf":"https://arxiv.org/pdf/2410.20460v1.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":"centralizers-in-the-plactic-monoid","repo_url":"https://github.com/wilsoa/Centralizers-in-the-Plactic-Monoid","is_official":1,"mentioned_in_paper":0,"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}