Stability of associated primes of integral closures of monomial ideals

Let I be a monomial ideal of a polynomial ring R=K[X"1,...,X"r] and d(I) the maximal degree of minimal generators of I. In this paper, we explicitly determine a number n"0 in terms of r and d(I) such that Ass(R/I^[email protected]?)=Ass(R/I^n^"^[email protected]?) for all n>=n"0. Furthermore, our n"0 is almost sharp.