Midwest Algebra, Geometry and their Interactions Conference MAGIC05 University of Notre Dame, Notre Dame October 7-11, 2005 Macauly and Green's theorems for ideals containing a regular sequence length two by Giulio CAVIGLIA, University of California at Berkeley Abstract: We study Hilbert functions of homogeneous ideals in K[x1, ..., xn] containing a regular sequence of given degrees d1, ..., dr. We present some progress in the direction of the Lex-Plus-Power conjecture. In the case r=2 we give a generalization of theorems of Macaulay and Green and in particular we characterize all the possible Hilbert functions of such ideals.