{"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/computing-character-tables-and-cartan","title":"Computing character tables and Cartan matrices of finite monoids with fixed point counting","arxiv_id":"2303.13647","date":"2023-03-23","proceeding":null,"authors":["Balthazar Charles"],"abstract":"In this paper we present an algorithm for efficiently counting fixed points in a finite monoid $M$ under a conjugacy-like action. We then prove a formula for the character table of $M$ in terms of fixed points and radical, which allows for the effective computation of the character table of $M$ over a field of null characteristic, as well as its Cartan matrix, using a formula from [Thi\\'ery '12], again in terms of fixed points. We discuss the implementation details of the resulting algorithms and provide benchmarks of their performances.","url_abs":"https://arxiv.org/abs/2303.13647v1","url_pdf":"https://arxiv.org/pdf/2303.13647v1.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":"computing-character-tables-and-cartan","repo_url":"https://github.com/zoltancoccyx/monoid-character-table","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}