{"paper":{"title":"Tverberg theorems over discrete sets of points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO"],"primary_cat":"math.MG","authors_text":"Fr\\'ed\\'eric Meunier, Jes\\'us A. De Loera, Nabil Mustafa, Thomas A. Hogan","submitted_at":"2018-03-05T18:22:58Z","abstract_excerpt":"This paper discusses Tverberg-type theorems with coordinate constraints (i.e., versions of these theorems where all points lie within a subset $S \\subset \\mathbb{R}^d$ and the intersection of convex hulls is required to have a non-empty intersection with $S$). We determine the $m$-Tverberg number, when $m \\geq 3$, of any discrete subset $S$ of $\\mathbb{R}^2$ (a generalization of an unpublished result of J.-P. Doignon). We also present improvements on the upper bounds for the Tverberg numbers of $\\mathbb{Z}^3$ and $\\mathbb{Z}^j \\times \\mathbb{R}^k$ and an integer version of the well-known posit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01816","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"}