{"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/the-insertion-encoding-of-cayley-permutations","title":"The insertion encoding of Cayley permutations","arxiv_id":"2505.08480","date":"2025-05-13","proceeding":null,"authors":["Christian Bean","Paul C. Bell","Abigail Ollson"],"abstract":"We introduce the vertical and horizontal insertion encodings for Cayley permutations which naturally generalise the insertion encoding for permutations. In both cases, we fully classify the Cayley permutation classes for which these languages are regular, and provide an algorithm for computing the rational generating functions. We use our algorithm to solve an open problem of Cerbai by enumerating the hare pop-stack sortable Cayley permutations.","url_abs":"https://arxiv.org/abs/2505.08480v1","url_pdf":"https://arxiv.org/pdf/2505.08480v1.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":"the-insertion-encoding-of-cayley-permutations","repo_url":"https://github.com/Ollson2921/cperms_ins_enc","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}