{"paper":{"title":"Helly numbers of Algebraic Subsets of $\\mathbb R^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"D. Oliveros, E. Rold\\'an-Pensado, J. A. De Loera, R. N. La Haye","submitted_at":"2015-08-10T19:57:10Z","abstract_excerpt":"We study $S$-convex sets, which are the geometric objects obtained as the intersection of the usual convex sets in $\\mathbb R^d$ with a proper subset $S\\subset \\mathbb R^d$. We contribute new results about their $S$-Helly numbers. We extend prior work for $S=\\mathbb R^d$, $\\mathbb Z^d$, and $\\mathbb Z^{d-k}\\times\\mathbb R^k$; we give sharp bounds on the $S$-Helly numbers in several new cases. We considered the situation for low-dimensional $S$ and for sets $S$ that have some algebraic structure, in particular when $S$ is an arbitrary subgroup of $\\mathbb R^d$ or when $S$ is the difference betw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02380","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"}