{"paper":{"title":"2-semiarcs in $\\mathrm{PG}(2,q)$, $q\\leq 13$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniele Bartoli, Fernanda Pambianco, Giorgio Faina, Gy\\\"orgy Kiss, Stefano Marcugini","submitted_at":"2014-07-22T09:38:01Z","abstract_excerpt":"A $2$-semiarc is a pointset ${\\mathcal S}_k$ with the property that the number of tangent lines to ${\\mathcal S}_k$ at each of its points is two. Using some theoretical results and computer aided search, the complete classification of $2$-semiarcs in PG$(2,q)$ is given for $q\\leq 7,$ the spectrum of their sizes is determined for $q\\leq 9$, and some results about the existence are proven for $q=11$ and $q=13.$ For several sizes of $2$-semiarcs in $\\mathrm{PG}(2,q)$, $q\\leq 7$, classification results have been obtained by theoretical proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5801","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"}