Maximal generating degrees of integral closures of powers of monomial ideals

We give effective lower and upper bounds on the maximal generating degree d(I^n) and the Castelnuovo–Mumford regularity reg (I^n) of the integral closure of a power I^n of a monomial ideal I for all n and determine the leading coefficient of the asymptotically linear functions d(I^n) and reg (I^n) . A number n_0 is also given such that d(I^n) becomes a linear function of n when n≥ n_0 .