{"paper":{"title":"Enumerating simplicial decompositions of surfaces with boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Juanjo Ru\\'e, Olivier Bernardi (LM-Orsay)","submitted_at":"2009-01-12T16:31:38Z","abstract_excerpt":"It is well-known that the triangulations of the disc with $n+2$ vertices on its boundary are counted by the $n$th Catalan number $C(n)=\\frac{1}{n+1}{2n \\choose n}$. This paper deals with the generalisation of this problem to any arbitrary compact surface $S$ with boundaries. We obtain the asymptotic number of simplicial decompositions of the surface $S$ with $n$ vertices on its boundary. More generally, we determine the asymptotic number of dissections of $S$ when the faces are $\\delta$-gons with $\\delta$ belonging to a set of admissible degrees $\\Delta\\subseteq \\{3,4,5,...\\}$. We also give th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1608","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"}