{"paper":{"title":"Non-crossing chords of a polygon with forbidden positions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Demin Zhang, Dongyi Wei, Dong Zhang","submitted_at":"2016-11-10T02:37:22Z","abstract_excerpt":"In this paper, we systematically study non-crossing chords of simple polygons in the plane. We first introduce the reduced Euler characteristic of a family of line-segments, and subsequently investigate the structure of the diagonals and epigonals of a polygon. Interestingly enough, the reduced Euler characteristic of a subfamily of diagonals and epigonals characterizes the geometric convexity of polygons. In particular, an alternative and complete answer is given for a problem proposed by G. C. Shephard. Meanwhile, we extend such research to non-crossing diagonals and epigonals with forbidden"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03166","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"}