Lattices generated by subspaces in d-bounded distance-regular graphs |
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Authors: | Jun Guo Suogang Gao Kaishun Wang |
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Institution: | aMathematics and Information College, Langfang Teachers’ College, Langfang 065000, PR China;bMathematics and Information College, Hebei Normal University, Shijiazhuang 050016, PR China;cSchool of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China |
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Abstract: | Let Γ denote a d-bounded distance-regular graph with diameter d 2. A regular strongly closed subgraph of Γ is said to be a subspace of Γ. Define the empty set to be the subspace with diameter -1 in Γ. For 0 i i+s d-1, let denote the set of all subspaces in Γ with diameters i,i+1,…,i+s including Γ and . If we define the partial order on by ordinary inclusion (resp. reverse inclusion), then is a poset, denoted by (resp. ). In the present paper we show that both and are atomic lattices, and classify their geometricity. |
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Keywords: | Distance-regular graph Subspaces Geometric lattice |
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