{"paper":{"title":"Counting Carambolas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Adrian Dumitrescu, Andr\\'e Schulz, Csaba D. T\\'oth, Maarten L\\\"offler","submitted_at":"2014-10-06T22:13:03Z","abstract_excerpt":"We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of $n$ points in the plane. Configurations of interest include \\emph{convex polygons}, \\emph{star-shaped polygons} and \\emph{monotone paths}. We also consider related problems for \\emph{directed} planar straight-line graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1579","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"}