{"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/arithmetic-infinite-friezes-from-punctured","title":"Arithmetic infinite friezes from punctured discs","arxiv_id":"1503.04352","date":"2015-03-14","proceeding":null,"authors":["Manuela Tschabold"],"abstract":"We define the notion of infinite friezes of positive integers as a variation of Conway-Coxeter frieze patterns and study their properties. We introduce useful gluing and cutting operations on infinite friezes. It turns out that triangulations of once-punctured discs give rise to periodic infinite friezes having special properties, a notable example being that each diagonal consists of a collection of arithmetic progressions. Furthermore, we work out a combinatorial interpretation of the entries of infinite friezes associated to triangulations of once-punctured discs via matching numbers for certain combinatorial objects, namely periodic triangulations of strips. Alternatively, we consider a known algorithm that as we show computes as well these entries.","url_abs":"http://arxiv.org/abs/1503.04352v3","url_pdf":"http://arxiv.org/pdf/1503.04352v3.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":"arithmetic-infinite-friezes-from-punctured","repo_url":"https://github.com/egunawan/friezepattern","is_official":0,"mentioned_in_paper":0,"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}