{"paper":{"title":"Large $\\{0, 1, \\ldots, t\\}$-Cliques in Dual Polar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ferdinand Ihringer, Klaus Metsch","submitted_at":"2015-10-06T18:48:02Z","abstract_excerpt":"We investigate $\\{0, 1, \\ldots, t \\}$-cliques of generators on dual polar graphs of finite classical polar spaces of rank $d$. These cliques are also known as Erd\\H{o}s-Ko-Rado sets in polar spaces of generators with pairwise intersections in at most codimension $t$. Our main result is that we classify all such cliques of maximum size for $t \\leq \\sqrt{8d/5}-2$ if $q \\geq 3$, and $t \\leq \\sqrt{8d/9}-2$ if $q = 2$. We have the following byproducts. (a) For $q \\geq 3$ we provide estimates of Hoffman's bound on these $\\{0, 1, \\ldots, t \\}$-cliques for all $t$. (b) For $q \\geq 3$ we determine the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01697","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"}