{"paper":{"title":"Permanent index of matrices associated with graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tsai-Lien Wong, Xuding Zhu","submitted_at":"2015-10-03T12:19:40Z","abstract_excerpt":"A total weighting of a graph $G$ is a mapping $f$ which assigns to each element $z \\in V(G) \\cup E(G)$ a real number $f(z)$ as its weight. The vertex sum of $v$ with respect to $f$ is $\\phi_f(v)=\\sum_{e \\in E(v)}f(e)+f(v)$. A total weighting is proper if $\\phi_f(u) \\ne \\phi_f(v)$ for any edge $uv$ of $G$. A $(k,k')$-list assignment is a mapping $L$ which assigns to each vertex $v$ a set $L(v)$ of $k$ permissible weights, and assigns to each edge $e$ a set $L(e)$ of $k'$ permissible weights. We say $G$ is $(k,k')$-choosable if for any $(k,k')$-list assignment $L$, there is a proper total weight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00810","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"}