Abstract
In this thesis we study a special kind of partially ordered sets which are called semi-Eulerian 2-strata posets (P, B). The posets possess many interesting results. There are two intrinsic properties, one is that the sub-poset B is a semi-Eulerian; the other one is that the ranks of B and P have different parity. The reciprocity law for these posets gives a formula on the zeta polynomials of P and B. With the reciprocity law, we deduce the generalized Dehn-Sommerville equations about the number of elements at various ranks of semi-Eulerian 2-strata posets. Moreover, we obtain the combinatorial Alexander duality which relates the Miibius function of P to the Mobius functions of B and any subposet Q of P.