{"paper":{"title":"Elation KM-arcs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, Maarten De Boeck","submitted_at":"2017-05-17T23:46:41Z","abstract_excerpt":"In this paper, we study KM-arcs in $PG(2, q)$, the Desarguesian projective plane of order $q$. A KM-arc A of type $t$ is a natural generalisation of a hyperoval: it is a set of $q + t$ points in $PG(2, q)$ such that every line of $PG(2,q)$ meets A in $0,2$ or $t$ points. We study a particular class of KM-arcs, namely, elation KM-arcs. These KM-arcs are highly symmetrical and moreover, many of the known examples are elation KM-arcs. We provide an algebraic framework and show that all elation KM-arcs of type $q/4$ in $PG(2,q)$ are translation KM-arcs. Using a result of [2], this concludes the cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06372","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"}