{"paper":{"title":"Perron-Frobenius Theorem for Rectangular Tensors and Directed Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arthur L.B. Yang, James J.Y. Zhao, Linyuan Lu","submitted_at":"2018-04-23T17:20:43Z","abstract_excerpt":"For any positive integers $r$, $s$, $m$, $n$, an $(r,s)$-order $(n,m)$-dimensional rectangular tensor ${\\cal A}=(a_{i_1\\cdots i_r}^{j_1\\cdots j_s}) \\in ({\\mathbb R}^n)^r\\times ({\\mathbb R}^m)^s$ is called partially symmetric if it is invariant under any permutation on the lower $r$ indexes and any permutation on the upper $s$ indexes. Such partially symmetric rectangular tensor arises naturally in studying directed hypergraphs. Ling and Qi [Front. Math. China, 2013] first studied the $(p,q)$-spectral radius (or singular values) and proved a Perron-Fronbenius theorem for such tensors when both "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08582","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"}