{"paper":{"title":"Bipartite Q-polynomial distance-regular graphs and uniform posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Paul Terwilliger, Stefko Miklavic","submitted_at":"2011-08-11T18:50:44Z","abstract_excerpt":"Let $\\G$ denote a bipartite distance-regular graph with vertex set $X$ and diameter $D \\ge 3$. Fix $x \\in X$ and let $L$ (resp. $R$) denote the corresponding lowering (resp. raising) matrix. We show that each $Q$-polynomial structure for $\\G$ yields a certain linear dependency among $RL^2$, $LRL$, $L^2R$, $L$. Define a partial order $\\le$ on $X$ as follows. For $y,z \\in X$ let $y \\le z$ whenever $\\partial(x,y)+\\partial(y,z)=\\partial(x,z)$, where $\\partial$ denotes path-length distance. We determine whether the above linear dependency gives this poset a uniform or strongly uniform structure. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2484","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"}