{"paper":{"title":"Projective Equivalences of k-neighbourly Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Larman, Natalia Garcia-Colin","submitted_at":"2013-03-15T04:29:10Z","abstract_excerpt":"We prove the following theorem, which is related to McMullen's problem on projective transformations of polytopes; let $2\\leq k\\leq \\lfloor{\\frac{d}{2}}\\rfloor$ and $\\nu{(d, k)}$ be the largest number such that any set of $\\nu{(d,k)}$ points lying in general position in $\\mathbb{R}^d$ can be mapped by a permissible projective transformation onto the vertices of a k-neighborly polytope, then $d + \\left\\lceil{\\frac{d}{k}}\\right\\rceil +1 \\leq \\nu{(d, k)} < 2d-k +1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3675","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"}