{"paper":{"title":"The spectral symmetry of weakly irreducible nonnegative tensors and connected hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chen-Lu Zhuan-Sun, Tao Huang, Yan-Hong Bao, Ya-Ping Li, Yi-Zheng Fan","submitted_at":"2017-04-28T03:40:53Z","abstract_excerpt":"Let $\\mathcal{A}$ be a weakly irreducible nonnegative tensor with spectral radius $\\rho(\\mathcal{A})$. Let $\\mathfrak{D}$ (respectively, $\\mathfrak{D}^{(0)}$) be the set of normalized diagonal matrices arising from the eigenvectors of $\\mathcal{A}$ corresponding to the eigenvalues with modulus $\\rho(\\mathcal{A})$ (respectively, the eigenvalue $\\rho(\\mathcal{A})$). It is shown that $\\mathfrak{D}$ is an abelian group containing $\\mathfrak{D}^{(0)}$ as a subgroup, which acts transitively on the set $\\{e^{\\mathbf{i} \\frac{2 \\pi j}{\\ell}}\\mathcal{A}:j =0,1, \\ldots,\\ell-1\\}$, where $|\\mathfrak{D}/\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08799","kind":"arxiv","version":3},"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"}