{"paper":{"title":"Triangulations of nearly convex polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Mouton (IF), Roland Bacher (IF)","submitted_at":"2010-12-10T08:54:18Z","abstract_excerpt":"Counting Euclidean triangulations with vertices in a finite set $\\C$ of the convex hull $\\conv(\\C)$ of $\\C$ is difficult in general, both algorithmically and theoretically. The aim of this paper is to describe nearly convex polygons, a class of configurations for which this problem can be solved to some extent. Loosely speaking, a nearly convex polygon is an infinitesimal perturbation of a weakly convex polygon (a convex polygon with edges subdivided by additional points). Our main result shows that the triangulation polynomial, enumerating all triangulations of a nearly convex polygon, is def"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2206","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"}