{"paper":{"title":"Normal cyclic polytopes and cyclic polytopes that are not very ample","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Lukas Katth\\\"an, Ryota Okazaki, Takayuki Hibi","submitted_at":"2012-02-28T05:30:50Z","abstract_excerpt":"Let $d$ and $n$ be positive integers with $n \\geq d + 1$ and $\\tau_{1}, ..., \\tau_{n}$ integers with $\\tau_{1} < ... < \\tau_{n}$. Let $C_{d}(\\tau_{1}, ..., \\tau_{n}) \\subset \\RR^{d}$ denote the cyclic polytope of dimension $d$ with $n$ vertices $(\\tau_{1},\\tau_{1}^{2},...,\\tau_{1}^{d}), ..., (\\tau_{n},\\tau_{n}^{2},...,\\tau_{n}^{d})$. We are interested in finding the smallest integer $\\gamma_{d}$ such that if $\\tau_{i+1} - \\tau_{i} \\geq \\gamma_{d}$ for $1 \\leq i < n$, then $C_{d}(\\tau_{1}, ..., \\tau_{n})$ is normal. One of the known results is $\\gamma_{d} \\leq d (d + 1)$. In the present paper a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6117","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"}