{"paper":{"title":"Characterization of isometric embeddings of Grassmann graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Pankov","submitted_at":"2012-03-01T07:29:46Z","abstract_excerpt":"Let $V$ be an $n$-dimensional left vector space over a division ring $R$. We write ${\\mathcal G}_{k}(V)$ for the Grassmannian formed by $k$-dimensional subspaces of $V$ and denote by $\\Gamma_{k}(V)$ the associated Grassmann graph. Let also $V'$ be an $n'$-dimensional left vector space over a division ring $R'$. Isometric embeddings of $\\Gamma_{k}(V)$ in $\\Gamma_{k'}(V')$ are classified in \\cite{Pankov2}. A classification of $J(n,k)$-subsets in ${\\mathcal G}_{k'}(V')$, i.e. the images of isometric embeddings of the Johnson graph $J(n,k)$ in $\\Gamma_{k'}(V')$, is presented in \\cite{Pankov1}. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0105","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"}