{"paper":{"title":"Point sets with many non-crossing matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CG","authors_text":"Andrei Asinowski, G\\\"unter Rote","submitted_at":"2015-02-17T15:28:52Z","abstract_excerpt":"The maximum number of non-crossing straight-line perfect matchings that a set of $n$ points in the plane can have is known to be $O(10.0438^n)$ and $\\Omega^*(3^n)$. The lower bound, due to Garc\\'ia, Noy, and Tejel (2000) is attained by the double chain, which has $\\Theta(3^n n^{O(1)})$ such matchings. We reprove this bound in a simplified way that uses the novel notion of down-free matching, and apply this approach on several other constructions. As a result, we improve the lower bound. First we show that double zigzag chain with $n$ points has $\\Theta^*(\\lambda^n)$ such matchings with $\\lambd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04925","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"}