{"paper":{"title":"The Non-Orientable Map Asymptotics Constant $p_g$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"S.R. Carrell","submitted_at":"2014-06-06T18:01:21Z","abstract_excerpt":"Using the pfaffian structure of the generating series for locally orientable maps, we show that the generating series satsifies a nonlinear differential equation called the BKP equation. Using this we are able to derive a cubic differential equation which is satisfied by the generating series for locally orientable triangulations. As a result, we prove a conjecture of Garoufalidis and Mari\\~no concerning the constant $p_g$ which appears in asymptotic formulas for a variety of rooted maps on non-orientable surfaces. This allows one to determine the asymptotic expansion for $p_g$ up to an unknow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1760","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"}