{"paper":{"title":"The multiplicity of eigenvalues of nonnegative weakly irreducible tensors and uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yi-Zheng Fan","submitted_at":"2024-10-28T08:28:50Z","abstract_excerpt":"Hu and Ye conjectured that for a $k$-th order and $n$-dimensional tensor $\\mathcal{A}$ with an eigenvalue $\\lambda$ and the corresponding eigenvariety $\\mathcal{V}_\\lambda(\\mathcal{A})$, $$\\mathrm{am}(\\lambda) \\ge \\sum_{i=1}^\\kappa \\mathrm{dim}(V_i)(k-1)^{\\mathrm{dim}(V_i)-1},$$ where $\\mathrm{am}(\\lambda)$ is the algebraic multiplicity of $\\lambda$, and $V_1,\\ldots,V_\\kappa$ are all irreducible components of $\\mathcal{V}_\\lambda(\\mathcal{A})$. In this paper, we prove that if $\\mathcal{A}$ is a nonnegative weakly irreducible tensor with spectral radius $\\rho$, then $\\mathrm{am}(\\lambda) \\ge |\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20830","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.20830/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}