Integral self-affine tiles in R-n .2. Lattice tilings

Let A be an expanding n x n integer matrix with \det(A)\ = m. A standard digit set D for A is any complete set of coset representatives for Z(n)/A(Z(n)). Associated to a given 2) is a set T(A, D), which is the attractor of an affine iterated function system, satisfying T = U (d is an element of D) (T + d) It is known that T(A, D) tiles R-n by some subset of Z(n). This paper proves that every standard digit set D gives a set T(A, D) that tiles R-n with a lattice tiling.