{"paper":{"title":"The $\\alpha$-normal labeling method for computing the $p$-spectral radii of uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lele Liu, Linyuan Lu","submitted_at":"2018-03-16T20:00:46Z","abstract_excerpt":"Let $G$ be an $r$-uniform hypergraph of order $n$. For each $p\\geq 1$, the $p$-spectral radius $\\lambda^{(p)}(G)$ is defined as \\[ \\lambda^{(p)}(G):=\\max_{|x_1|^p+\\cdots+|x_n|^p=1} r\\sum_{\\{i_1,\\ldots,i_r\\}\\in E(G)}x_{i_1}\\cdots x_{i_r}. \\] The $p$-spectral radius was introduced by Keevash-Lenz-Mubayi, and subsequently studied by Nikiforov in 2014. The most extensively studied case is when $p=r$, and $\\lambda^{(r)}(G)$ is called the spectral radius of $G$. The $\\alpha$-normal labeling method, which was introduced by Lu and Man in 2014, is effective method for computing the spectral radii of un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06385","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"}