{"paper":{"title":"Graph homomorphisms on rectangular matrices over division rings II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kang Zhao, Li-Ping Huang","submitted_at":"2017-02-19T05:39:20Z","abstract_excerpt":"Let ${\\mathbb{D}}^{m\\times n}$ be the set of $m\\times n$ matrices over a division ring $\\mathbb{D}$. Two matrices $A,B\\in {\\mathbb{D}}^{m\\times n}$ are adjacent if ${\\rm rank}(A-B)=1$. By the adjacency, ${\\mathbb{D}}^{m\\times n}$ is a connected graph. Suppose $\\mathbb{D}, \\mathbb{D}'$ are division rings and $m,n,m',n'\\geq2$ are integers. We determine additive graph homomorphisms from ${\\mathbb{D}}^{m\\times n}$ to ${\\mathbb{D}'}^{m'\\times n'}$. When $|\\mathbb{D}|\\geq 4$, we characterize the graph homomorphism $\\varphi: {\\mathbb{D}}^{n\\times n}\\rightarrow {\\mathbb{D}'}^{m'\\times n'}$ if $\\varphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05703","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"}