{"paper":{"title":"Some new trace formulas of tensors with applications in spectral hypergraph theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Jia-Yu Shao, Liqun Qi, Shenglong Hu","submitted_at":"2013-07-22T13:01:23Z","abstract_excerpt":"We give some graph theoretical formulas for the trace $Tr_k(\\mathbb {T})$ of a tensor $\\mathbb {T}$ which do not involve the differential operators and auxiliary matrix. As applications of these trace formulas in the study of the spectra of uniform hypergraphs, we give a characterization (in terms of the traces of the adjacency tensors) of the $k$-uniform hypergraphs whose spectra are $k$-symmetric, thus give an answer to a question raised in [3]. We generalize the results in [3, Theorem 4.2] and [5, Proposition 3.1] about the $k$-symmetry of the spectrum of a $k$-uniform hypergraph, and answe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5690","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"}