{"paper":{"title":"Association schemes on the Schubert cells of a Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yuta Watanabe","submitted_at":"2017-11-17T09:06:06Z","abstract_excerpt":"Let $\\mathbb{F}$ be any field. The Grassmannian $\\mathrm{Gr}(m,n)$ is the set of $m$-dimensional subspaces in $\\mathbb{F}^n$, and the general linear group $\\mathrm{GL}_n(\\mathbb{F})$ acts transitively on it. The Schubert cells of $\\mathrm{Gr}(m,n)$ are the orbits of the Borel subgroup $\\mathcal{B} \\subset \\mathrm{GL}_n(\\mathbb{F})$ on $\\mathrm{Gr}(m,n)$. We consider the association scheme on each Schubert cell defined by the $\\mathcal{B}$-action and show it is symmetric and it is the generalized wreath product of one-class association schemes, which was introduced by R. A. Bailey [European Jou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06462","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"}