{"paper":{"title":"On Disjoint hypercubes in Fibonacci cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michel Mollard (IF), Sara Zemljic, Simon Spacapan, Sylvain Gravier (IF)","submitted_at":"2015-04-03T12:20:55Z","abstract_excerpt":"The {\\em Fibonacci cube} of dimension $n$, denoted as $\\Gamma\\_n$,  is the subgraph of  $n$-cube $Q\\_n$ induced by vertices with no consecutive 1's. We study the maximum number of disjoint subgraphs in $\\Gamma\\_n$ isomorphic to $Q\\_k$, and denote this number by $q\\_k(n)$. We prove several recursive results for $q\\_k(n)$, in particular we prove that \n$q\\_{k}(n) = q\\_{k-1}(n-2) + q\\_{k}(n-3)$. We also prove a closed formula in which $q\\_k(n)$ is given in terms of  Fibonacci numbers, and finally we give the generating function for the sequence  $\\{q\\_{k}(n)\\}\\_{n=0}^{ \\infty}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00829","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}