{"paper":{"title":"A combinatorial interpretation of the $\\kappa^{\\star}_{g}(n)$ coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, Thomas J. X. Li","submitted_at":"2014-06-12T09:25:16Z","abstract_excerpt":"Studying the virtual Euler characteristic of the moduli space of curves, Harer and Zagier compute the generating function $C_g(z)$ of unicellular maps of genus $g$. They furthermore identify coefficients, $\\kappa^{\\star}_{g}(n)$, which fully determine the series $C_g(z)$. The main result of this paper is a combinatorial interpretation of $\\kappa^{\\star}_{g}(n)$. We show that these enumerate a class of unicellular maps, which correspond $1$-to-$2^{2g}$ to a specific type of trees, referred to as O-trees. O-trees are a variant of the C-decorated trees introduced by Chapuy, F\\'{e}ray and Fusy. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3162","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"}