Extremal Betti numbers of graded ideals

The possible extremal Betti numbers of graded ideals in the polynomial ring K[x₁,…,x_n] in n variables with coefficients in a field K are studied, completing our results in [7]. In case char(K) = 0 we determine, given any integers r < n, the conditions under which there exists a graded ideal I ? K[x₁,…, x_n] with extremal Betti numbers $beta_{k_{i}k_{i}+ell_{i}} {rm for} i=1,cdots,r$ . We also treat a similar problem for squarefree lexsegment ideals.