{"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/an-efficient-algorithm-computing-composition","title":"An efficient algorithm computing composition factors of $T(V)^{\\otimes n}$","arxiv_id":"1711.04326","date":"2017-11-12","proceeding":null,"authors":["Amin Saied"],"abstract":"We present an algorithm that computes the composition factors of the n-th tensor power of the free associative algebra on a vector space. The composition factors admit a description in terms of certain coefficients $c_{\\lambda\\mu}$ determining their irreducible structure. By reinterpreting these coefficients as counting the number of ways to solve certain `decomposition-puzzles' we are able to design an efficient algorithm extending the range of computation by a factor of over 750. Furthermore, by visualising the data appropriately, we gain insights into the nature of the coefficients leading to the development of a new representation theoretic framework called PD-modules.","url_abs":"http://arxiv.org/abs/1711.04326v1","url_pdf":"http://arxiv.org/pdf/1711.04326v1.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":"an-efficient-algorithm-computing-composition","repo_url":"https://github.com/aminsaied/composition_factors","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}