{"paper":{"title":"On the Class of Similar Square {-1,0,1}-Matrices Arising from Vertex maps on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bau-Sen Du","submitted_at":"2015-03-16T08:29:34Z","abstract_excerpt":"Let $n \\ge 2$ be an integer. In this note, we show that the {\\it oriented} transition matrices over the field $\\mathcal R$ of all real numbers (over the finite field $\\mathcal Z_2$ of two elements respectively) of all continuous {\\it vertex maps} on {\\it all} oriented trees with $n+1$ vertices are similar to one another over $\\mathcal R$ (over $\\mathcal Z_2$ respectively) and have characteristic polynomial $\\sum_{k=0}^n x^k$. Consequently, the {\\it unoriented} transition matrices over the field $Z_2$ of all continuous {\\it vertex maps} on {\\it all} oriented trees with $n+1$ vertices are simila"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04568","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"}