Let P be the finite partially ordered set with rank function. The LYM property (including the equivalently normalized matching and regular covering properties) and the logarithmically convex property of its Whitney nu...Let P be the finite partially ordered set with rank function. The LYM property (including the equivalently normalized matching and regular covering properties) and the logarithmically convex property of its Whitney number are rather important in the study of combinatorial order theory. The Sperner property can be deduced from LYM property. Let B_n be Boolean algebra, and A, B∈B_n,(LA)={x∈B_n,x(?)A},M(B)={x∈B_n,x(?)B} are the order filter and order ideal generated by A and B, respectively.展开更多
文摘Let P be the finite partially ordered set with rank function. The LYM property (including the equivalently normalized matching and regular covering properties) and the logarithmically convex property of its Whitney number are rather important in the study of combinatorial order theory. The Sperner property can be deduced from LYM property. Let B_n be Boolean algebra, and A, B∈B_n,(LA)={x∈B_n,x(?)A},M(B)={x∈B_n,x(?)B} are the order filter and order ideal generated by A and B, respectively.