{"paper":{"title":"On transversal and 2-packing numbers in uniform linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adri\\'an V\\'azquez-\\'Avila, Carlos A. Alfaro, C. Rubio-Montiel, G. Araujo-Pardo","submitted_at":"2019-03-19T18:47:56Z","abstract_excerpt":"A linear system is a pair $(P,\\mathcal{L})$ where $\\mathcal{L}$ is a family of subsets on a ground finite set $P$, such that $|l\\cap l^\\prime|\\leq 1$, for every $l,l^\\prime \\in \\mathcal{L}$. The elements of $P$ and $\\mathcal{L}$ are called points and lines, respectively, and the linear system is called intersecting if any pair of lines intersect in exactly one point. A subset $T$ of points of $P$ is a transversal of $(P,\\mathcal{L})$ if $T$ intersects any line, and the transversal number, $\\tau(P,\\mathcal{L})$, is the minimum order of a transversal. On the other hand, a 2-packing set of a line"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08984","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"}