{"paper":{"title":"Classification of k-nets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G. Korchm\\'aros, G. P. Nagy","submitted_at":"2016-01-29T09:11:34Z","abstract_excerpt":"A finite \\emph{$k$-net} of order $n$ is an incidence structure consisting of $k\\ge 3$ pairwise disjoint classes of lines, each of size $n$, such that every point incident with two lines from distinct classes is incident with exactly one line from each of the $k$ classes. Deleting a line class from a $k$-net, with $k\\ge 4$, gives a \\emph{derived} ($k-1$)-net of the same order.\n  Finite $k$-nets embedded in a projective plane $PG(2,K)$ coordinatized by a field $K$ of characteristic $0$ only exist for $k=3,4$, see \\cite{knp_k}. In this paper, we investigate $3$-nets embedded in $PG(2,K)$ whose li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08009","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"}