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Bipartite Q-polynomial distance-regular graphs and uniform posets
[article]

2011
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arXiv
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pre-print

Let denote a bipartite distance-regular graph with vertex set X and diameter D > 3. Fix x ∈ X and let L (resp. R) denote the corresponding lowering (resp. raising) matrix. We show that each Q-polynomial structure for yields a certain linear dependency among RL^2, LRL, L^2R, L. Define a partial order < on X as follows. For y,z ∈ X let y < z whenever ∂(x,y)+∂(y,z)=∂(x,z), where ∂ denotes path-length distance. We determine whether the above linear dependency gives this poset a uniform or strongly

arXiv:1108.2484v1
fatcat:tfxrnwpntzfqdmze63wbrrsysi