{"paper":{"title":"Classification of crescent configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chi Huynh, Eyvindur A. Palsson, Max Hlavacek, Rebecca F. Durst, Steven J. Miller","submitted_at":"2016-10-25T11:34:31Z","abstract_excerpt":"Let $n$ points be in crescent configurations in $\\mathbb{R}^d$ if they lie in general position in $\\mathbb{R}^d$ and determine $n-1$ distinct distances, such that for every $1 \\leq i \\leq n-1$ there is a distance that occurs exactly $i$ times. Since Erd\\H{o}s' conjecture in 1989 on the existence of $N$ sufficiently large such that no crescent configurations exist on $N$ or more points, he, Pomerance, and Pal\\'asti have given constructions for $n$ up to $8$ but nothing is yet known for $n \\geq 9$. Most recently, Burt et. al. had proven that a crescent configuration on $n$ points exists in $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07836","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"}