{"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/constructing-unlabelled-lattices","title":"Constructing unlabelled lattices","arxiv_id":"1609.08255","date":"2016-09-27","proceeding":null,"authors":["Volker Gebhardt","Stephen Tawn"],"abstract":"We present an improved orderly algorithm for constructing all unlabelled lattices up to a given size, that is, an algorithm that constructs the minimal element of each isomorphism class relative to some total order. Our algorithm employs a stabiliser chain approach for cutting branches of the search space that cannot contain a minimal lattice; to make this work, we grow lattices by adding a new layer at a time, as opposed to adding one new element at a time, and we use a total order that is compatible with this modified strategy. The gain in speed is between one and two orders of magnitude. As an application, we compute the number of unlabelled lattices on 20 elements.","url_abs":"http://arxiv.org/abs/1609.08255v3","url_pdf":"http://arxiv.org/pdf/1609.08255v3.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":"constructing-unlabelled-lattices","repo_url":"https://bitbucket.org/vgebhardt/unlabelled-lattices","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}