{"paper":{"title":"The $(p,q)$-spectral radii of $(r,s)$-directed 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":"2018-04-24T01:58:18Z","abstract_excerpt":"An $(r,s)$-directed hypergraph is a directed hypergraph with $r$ vertices in tail and $s$ vertices in head of each arc. Let $G$ be an $(r,s)$-directed hypergraph. For any real numbers $p$, $q\\geq 1$, we define the $(p,q)$-spectral radius $\\lambda_{p,q}(G)$ as \\[ \\lambda_{p,q}(G):=\\max_{||{\\bf x}||_p=||{\\bf y}||_q=1} \\sum_{e\\in E(G)}\\Bigg(\\prod_{u\\in T(e)}x_u\\Bigg)\\Bigg(\\prod_{v\\in H(e)}y_v\\Bigg), \\] where ${\\bf x}=(x_1, \\ldots, x_m)^{{\\rm T}}$, ${\\bf y}=(y_1,\\ldots, y_n)^{{\\rm T}}$ are real vectors; and $T(e)$, $H(e)$ are the tail and head of arc $e$, respectively. We study some properties abo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08808","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"}