{"paper":{"title":"Partial covers of PG(n,q)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, Leo Storme, Stefan Dodunekov","submitted_at":"2012-10-03T06:31:09Z","abstract_excerpt":"In this paper, we show that a set of q+a hyperplanes, q>13, a<(q-10)/4, that does not cover PG(n,q), does not cover at least q^(n-1)-aq^(n-2) points, and show that this lower bound is sharp. If the number of non- covered points is at most q^(n-1), then we show that all non-covered points are contained in one hyperplane. Finally, using a recent result of Blokhuis, Brouwer, and Szonyi [3], we remark that the bound on a for which these results are valid can be improved to a<(q-2)/3 and that this upper bound on a is sharp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1002","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"}