The Folded(2D+1)-cube and Its Uniform Posets  

作　　者：Li-hang HOU BO HOU Suo-gang GAO 

机构地区：[1]College of Mathematics and Information Science, Hebei Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2018年第2期281-292,共12页应用数学学报（英文版）

基　　金：Supported by the Natural Science Foundation of China(No.11471097);the Innovative Fund Project of Hebei Province(sj.2017084)

摘　　要：Let F denote the folded （2D ＋ 1）-cube with vertex set X and diameter D ≥ 3. Fix x∈ X. We first define a partial order ≤ on X as follows. For y,z ∈ X let y ≤ z whenever （x,y）＋ （y,z） =- （x, z）. Let R （resp. L） denote the raising matrix （resp. lowering matrix） of P. Next we show that there exists a certain linear dependency among RL2, LRL, L2R and L for each given Q-polynomial structure of F. Finally, we determine whether the above linear dependency structure gives this poser a uniform structure or strongly uniform structure.Let F denote the folded （2D ＋ 1）-cube with vertex set X and diameter D ≥ 3. Fix x∈ X. We first define a partial order ≤ on X as follows. For y,z ∈ X let y ≤ z whenever （x,y）＋ （y,z） =- （x, z）. Let R （resp. L） denote the raising matrix （resp. lowering matrix） of P. Next we show that there exists a certain linear dependency among RL2, LRL, L2R and L for each given Q-polynomial structure of F. Finally, we determine whether the above linear dependency structure gives this poser a uniform structure or strongly uniform structure.

关 键 词：distance-regular graph the folded （2D ＋ 1）-cube uniform poset 

分 类 号：O153.1[理学—数学]