{"paper":{"title":"Isometric embeddings of half-cube graphs in half-spin Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Pankov","submitted_at":"2011-06-27T16:35:53Z","abstract_excerpt":"Let $\\Pi$ be a polar space of type $\\textsf{D}_{n}$. Denote by ${\\mathcal G}_{\\delta}(\\Pi)$, $\\delta\\in \\{+,-\\}$ the associated half-spin Grassmannians and write $\\Gamma_{\\delta}(\\Pi)$ for the corresponding half-spin Grassmann graphs. In the case when $n\\ge 4$ is even, the apartments of ${\\mathcal G}_{\\delta}(\\Pi)$ will be characterized as the images of isometric embeddings of the half-cube graph $\\frac{1}{2}H_n$ in $\\Gamma_{\\delta}(\\Pi)$. As an application, we describe all isometric embeddings of $\\Gamma_{\\delta}(\\Pi)$ in the half-spin Grassmann graphs associated to a polar space of type $\\te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5435","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":""},"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"}