{"paper":{"title":"Partition functions and a generalized coloring-flow duality for embedded graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bart Litjens, Bart Sevenster","submitted_at":"2017-01-02T15:31:50Z","abstract_excerpt":"Let $G$ be a finite group and $\\chi: G \\rightarrow \\mathbb{C}$ a class function. Let $H = (V,E)$ be a directed graph with for each vertex a cyclic order of the edges incident to it. The cyclic orders give a collection $F$ of faces of $H$. Define the partition function $P_{\\chi}(H) := \\sum_{\\kappa: E \\rightarrow G}\\prod_{v \\in V}\\chi(\\kappa(\\delta(v)))$, where $\\kappa(\\delta(v))$ denotes the product of the $\\kappa$-values of the edges incident with $v$ (in order), where the inverse is taken for any edge leaving $v$. Write $\\chi = \\sum_{\\lambda}m_{\\lambda}\\chi_{\\lambda}$, where the sum runs over"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00420","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"}