{"paper":{"title":"Identities between dimer partition functions on different surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Anh Minh Pham, David Cimasoni","submitted_at":"2016-08-02T09:02:06Z","abstract_excerpt":"Given a weighted graph $G$ embedded in a non-orientable surface $\\Sigma$, one can consider the corresponding weighted graph $\\widetilde{G}$ embedded in the so-called orientation cover $\\widetilde\\Sigma$ of $\\Sigma$. We prove identities relating twisted partition functions of the dimer model on these two graphs. When $\\Sigma$ is the M\\\"obius strip or the Klein bottle, then $\\widetilde\\Sigma$ is the cylinder or the torus, respectively, and under some natural assumptions, these identities imply relations between the genuine dimer partition functions $Z(G)$ and $Z(\\widetilde{G})$. For example, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00741","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"}