Incomparability and intersection properties of Boolean interval lattices and chain posets

In a canonical way, we establish an AZ-identity (see [2]) and its consequences, the LYM-inequality and the Sperner property, for the Boolean interval lattice. Furthermore, the Bollobas inequality for the Boolean interval lattice turns out to be just the LYM-inequality for the Boolean lattice. We also present an Intersection Theorem for this lattice. Perhaps more surprising is that by our approach the conjecture of P. L. Erdos ei al. [7] and Z. Furedi concerning an Erdos-Ko-Rado-type intersection property for the poset of Boolean chains could also be established. In fact, we give two seemingly elegant proofs. (C) 1996 Academic Press Limited