{"paper":{"title":"Codimension two and three 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 (1), Jorge Luis Ram\\'irez Alfons\\'in (1) ((1) IMAG), Leonardo Mart\\'inez-Sandoval (1), Luis Montejano, Luis Pedro Montejano (1)","submitted_at":"2016-01-04T09:32:25Z","abstract_excerpt":"Let $k,d,\\lambda \\geqslant 1$ be integers with $d\\geqslant \\lambda $ and let $X$ be a finite set of points in $\\mathbb{R}^{d}$. A $(d-\\lambda)$-plane $L$ transversal to the convex hulls of all $k$-sets of $X$ is called Kneser transversal. If in addition $L$ contains $(d-\\lambda)+1$ points of $X$, then $L$ is  called complete Kneser transversal.In this paper, we present various results on the existence of (complete) Kneser transversals for $\\lambda =2,3$.  In order to do this, we introduce the notions of stability and instability for (complete) Kneser transversals. We first give a stability res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00421","kind":"arxiv","version":4},"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"}