{"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/configurations-of-higher-orders","title":"Configurations of higher orders","arxiv_id":"2203.12528","date":"2022-03-23","proceeding":null,"authors":["Benjamin Peet"],"abstract":"This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further extension to the notion of points and $k$-planes ($k$-dimensional hyperplanes) which we refer to as configurations of order $k$. We present a number of general examples such as stacked configurations of order $k$ - intuitively layering lower order configurations - and product configurations of order $k$. We discuss many analogues of standard configurations such as dual configurations, isomorphisms, graphical representations, and when a configuration is geometric. We focus mostly on configurations of order $2$ and specifically compute the number of possible symmetric configurations of order $2$ when each plane contains $3$ points for small values on $n$ - the total number of points in the configuration.","url_abs":"https://arxiv.org/abs/2203.12528v1","url_pdf":"https://arxiv.org/pdf/2203.12528v1.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":"configurations-of-higher-orders","repo_url":"https://github.com/benjaminpeet/configurationsofhigherorders","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}