{"paper":{"title":"Complete Kneser Transversals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.MG"],"primary_cat":"math.CO","authors_text":"Jonathan Chappelon (IMAG), Jorge Luis Ram\\'irez Alfons\\'in (IMAG), Leonardo Mart\\'inez-Sandoval (IMAG), Luis Montejano, Luis Pedro Montejano (IMAG)","submitted_at":"2015-11-04T12:55:48Z","abstract_excerpt":"Let $k,d,\\lambda\\geqslant1$ be integers with $d\\geqslant\\lambda $. Let $m(k,d,\\lambda)$ be the maximum positive integer $n$ such that every set of $n$ points (not necessarily in general position) in $\\mathbb{R}^{d}$ has the property that the convex hulls of all $k$-sets have a common transversal $(d-\\lambda)$-plane. It turns out that  $m(k, d,\\lambda)$ is strongly connected with other interesting problems, for instance, the chromatic number of Kneser hypergraphs and a discrete version of Rado's centerpoint theorem. In the same spirit, we introduce a natural discrete version $m^*$ of $m$ by con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01315","kind":"arxiv","version":3},"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"}