{"paper":{"title":"A bijection for covered maps, or a shortcut between Harer-Zagier's and Jackson's formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guillaume Chapuy, Olivier Bernardi (MIT)","submitted_at":"2010-01-11T06:06:16Z","abstract_excerpt":"We consider maps on orientable surfaces. A map is called \\emph{unicellular} if it has a single face. A \\emph{covered map} is a map (of genus $g$) with a marked unicellular spanning submap (which can have any genus in $\\{0,1,...,g\\}$). Our main result is a bijection between covered maps with $n$ edges and genus $g$ and pairs made of a plane tree with $n$ edges and a unicellular bipartite map of genus $g$ with $n+1$ edges. In the planar case, covered maps are maps with a marked spanning tree and our bijection specializes into a construction obtained by the first author in \\cite{OB:boisees}. Cove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1592","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"}