{"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/some-exact-values-of-the-inducibility-and","title":"Some exact values of the inducibility and statistics constants for hypercubes","arxiv_id":"2503.03408","date":"2025-03-05","proceeding":null,"authors":["Levente Bodnár","Oleg Pikhurko"],"abstract":"We consider two types of problems: maximising, over subsets $S\\subseteq \\{0,1\\}^n$, the density of $d$-subcubes $C$ in the $n$-hypercube graph that span a subgraph such that $S\\cap C$ is i) isomorphic to the given configuration $H\\subseteq\\{0,1\\}^d$ (the inducibility problem), or ii) has the given size $s$ (the statistics problem). Using flag algebras, we determine the limit of this density as $n\\to\\infty$ for 5 new configurations $H\\subseteq\\{0,1\\}^3$ and for 3 new pairs $(d,s)$, namely for $(3,2)$, $(4,2)$ and $(4,4)$. Interestingly, the lower bounds in the last three cases come from blowups of small Hamming codes.","url_abs":"https://arxiv.org/abs/2503.03408v2","url_pdf":"https://arxiv.org/pdf/2503.03408v2.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":"some-exact-values-of-the-inducibility-and","repo_url":"https://github.com/bodnalev/supplementary_files","is_official":1,"mentioned_in_paper":0,"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}