{"paper":{"title":"On terminal forms for topological polynomials for ribbon graphs: The $N$-petal flower","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Etera R. Livine, Joseph Ben Geloun, Remi C. Avohou","submitted_at":"2012-12-24T20:09:52Z","abstract_excerpt":"The Bollobas-Riordan polynomial [Math. Ann. 323, 81 (2002)] extends the Tutte polynomial and its contraction/deletion rule for ordinary graphs to ribbon graphs. Given a ribbon graph $\\cG$, the related polynomial should be computable from the knowledge of the terminal forms of $\\cG$ namely specific induced graphs for which the contraction/deletion procedure becomes more involved. We consider some classes of terminal forms as rosette ribbon graphs with $N\\ge 1$ petals and solve their associate Bollobas-Riordan polynomial. This work therefore enlarges the list of terminal forms for ribbon graphs "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5961","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"}