{"paper":{"title":"Omnimosaics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Anant P. Godbole, Katie R. Banks, Nicholas George Triantafillou","submitted_at":"2010-09-23T14:57:01Z","abstract_excerpt":"An {\\it omnimosaic} $O(n,k,a)$ is defined to be an $n\\times n$ matrix, with entries from the set ${\\cal A}=\\{1,2,\\...,a\\}$, that contains, as a submatrix, each of the $a^{k^2}$ $k\\times k$ matrices over ${\\cal A}$. We provide constructions of omnimosaics and show that for fixed $a$ the smallest possible size $\\omega(k,a)$ of an $O(n,k,a)$ omnimosaic satisfies \\[\\frac{ka^{k/2}}{e}\\le \\omega(k,a)\\le \\frac{ka^{k/2}}{e}(1+o(1))\\] for a well-specified function $o(1)$ that tends to zero as $k\\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4626","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"}