{"paper":{"title":"Computing the permanental polynomials of bipartite graphs by Pfaffian orientation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heping Zhang, Wei Li","submitted_at":"2010-10-06T10:21:16Z","abstract_excerpt":"The permanental polynomial of a graph $G$ is $\\pi(G,x)\\triangleq\\mathrm{per}(xI-A(G))$. From the result that a bipartite graph $G$ admits an orientation $G^e$ such that every cycle is oddly oriented if and only if it contains no even subdivision of $K_{2,3}$, Yan and Zhang showed that the permanental polynomial of such a bipartite graph $G$ can be expressed as the characteristic polynomial of the skew adjacency matrix $A(G^e)$. In this paper we first prove that this equality holds only if the bipartite graph $G$ contains no even subdivision of $K_{2,3}$. Then we prove that such bipartite graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1113","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"}