{"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/counting-sub-multisets-of-fixed-cardinality","title":"Counting sub-multisets of fixed cardinality","arxiv_id":"1511.06142","date":"2015-11-19","proceeding":null,"authors":["Sebastiano Ferraris","Alex Mendelson","Gerardo Ballesio","Tom Vercauteren"],"abstract":"This report presents an expression for the number of a multiset's sub-multisets of a given cardinality as a function of the multiplicity of its elements. This is also the number of distinct samples of a given size that may be produced by sampling without replacement from a finite population partitioned into subsets, in the case where items belonging to the same subset are considered indistinguishable. Despite the generality of this problem, we have been unable to find this result published elsewhere.","url_abs":"https://arxiv.org/abs/1511.06142v1","url_pdf":"https://arxiv.org/pdf/1511.06142v1.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":"counting-sub-multisets-of-fixed-cardinality","repo_url":"https://github.com/SebastianoF/counting_sub_multisets","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}