{"paper":{"title":"Annular Non-Crossing Matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Paul Drube, Puttipong Pongtanapaisan","submitted_at":"2015-08-07T14:50:45Z","abstract_excerpt":"It is well known that the number of distinct non-crossing matchings of $n$ half-circles in the half-plane with endpoints on the x-axis equals the $n^{th}$ Catalan number $C_n$. This paper generalizes that notion of linear non-crossing matchings, as well as the circular non-crossings matchings of Goldbach and Tijdeman, to non-crossings matchings of $n$ line segments embedded within an annulus. We prove that the number of such matchings $\\vert Ann(n,m) \\vert$ with $n$ exterior endpoints and $m$ interior endpoints correspond to an entirely new, one-parameter generalization of the Catalan numbers "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01712","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"}