{"paper":{"title":"The transition matroid of a 4-regular graph: an introduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lorenzo Traldi","submitted_at":"2013-07-30T19:32:57Z","abstract_excerpt":"Given a 4-regular graph $F$, we introduce a binary matroid $M_{\\tau}(F)$ on the set of transitions of $F$. Parametrized versions of the Tutte polynomial of $M_{\\tau}(F)$ yield several well-known graph and knot polynomials, including the Martin polynomial, the homflypt polynomial, the Kauffman polynomial and the Bollob\\'as-Riordan polynomial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8097","kind":"arxiv","version":7},"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"}