{"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/linked-partition-ideals-and-the-alladi-schur","title":"Linked partition ideals and the Alladi--Schur theorem","arxiv_id":"2110.13247","date":"2021-10-25","proceeding":null,"authors":["George E. Andrews","Shane Chern","Zhitai Li"],"abstract":"Let $\\mathscr{S}$ denote the set of integer partitions into parts that differ by at least $3$, with the added constraint that no two consecutive multiples of $3$ occur as parts. We derive trivariate generating functions of Andrews--Gordon type for partitions in $\\mathscr{S}$ with both the number of parts and the number of even parts counted. In particular, we provide an analytic counterpart of Andrews' recent refinement of the Alladi--Schur theorem.","url_abs":"https://arxiv.org/abs/2110.13247v1","url_pdf":"https://arxiv.org/pdf/2110.13247v1.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":"linked-partition-ideals-and-the-alladi-schur","repo_url":"https://github.com/shanechern/alladi-schur","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}