Artinian level algebras of codimension 3

In this paper, we continue the study of which h-vectors can be the Hilbert function of a level algebra by investigating Artinian level algebras of codimension 3 with the condition , where is the lex-segment ideal associated with an ideal I. Our approach is to adopt a homological method called the Cancellation Principle: the minimal free resolution of I is obtained from that of by canceling some adjacent terms of the same shift.We prove that when , R/I can be an Artinian level k-algebra only if either hd−1