{"paper":{"title":"Semiarcs with a long secant in $\\mathrm{PG}(2,q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bence Csajb\\'ok, Gy\\\"orgy Kiss, Tam\\'as H\\'eger","submitted_at":"2013-10-27T16:05:01Z","abstract_excerpt":"A $t$-semiarc is a pointset ${\\cal S}_t$ with the property that the number of tangent lines to ${\\cal S}_t$ at each of its points is $t$. We show that if a small $t$-semiarc ${\\cal S}_t$ in $\\mathrm{PG}(2,q)$ has a large collinear subset ${\\cal K}$, then the tangents to ${\\cal S}_t$ at the points of ${\\cal K}$ can be blocked by $t$ points not in ${\\cal K}$. We also show that small $t$-semiarcs are related to certain small blocking sets. Some characterization theorems for small semiarcs with large collinear subsets in $\\mathrm{PG}(2,q)$ are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7207","kind":"arxiv","version":2},"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"}