On the mixed multiplicity and the multiplicity of blow-up rings of equimultiple ideals

Let be a graded algebra of dimension d generated by finitely many elements of degree 1 over a field k and a homogeneous equimultiple ideal I of S with htI=h>0. In this paper we will show that if a1 a2 ah is the degree sequence of a minimal homogeneous reduction of I, then the mixed multiplicity for all 0