{"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/numerical-semigroups-with-embedding-dimension","title":"Numerical semigroups with embedding dimension three and minimal catenary degree","arxiv_id":"1909.09419","date":"2019-09-20","proceeding":null,"authors":["Pedro A. García-Sánchez","Helena Martín-Cruz"],"abstract":"We characterize numerical semigroups $S$ with embedding dimension three attaining equality in the inequality $\\max\\Delta(S)+2\\leq \\operatorname{cat}(S)$, where $\\Delta(S)$ denotes the Delta set of $S$ and $\\operatorname{cat}(S)$ denotes the catenary degree of $S$.","url_abs":"http://arxiv.org/abs/1909.09419v1","url_pdf":"http://arxiv.org/pdf/1909.09419v1.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":"numerical-semigroups-with-embedding-dimension","repo_url":"https://github.com/helenahmc/Examples-min-cat-deg","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}