{"paper":{"title":"On the genus filtration of diagrams over two backbones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Mingming Fu, Christian M. Reidys","submitted_at":"2013-11-04T12:54:23Z","abstract_excerpt":"In this paper we compute the bivariate generating function of $\\gamma$-matchings over two backbones, filtered by the number of arcs and the topological genus. $\\gamma$-matchings over two backbones are chord-diagrams, obtained via concatenation and nesting of irreducible shapes of topological genus $\\le \\gamma$. We show that the key information is contained in the polynomials counting these shapes and provide recursions that allow to compute the latter. In particular we give a bijection between such irreducible shapes over one and two backbones. We present two applications of our results. The f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0682","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"}