A Finite Basis Theorem Revisited

摘要

Let S denote a set of k-dimensional boxes each having integral sides. Let gamma(S) denote the set of all boxes which can be filled completely with translates of elements of S. It is shown here that S contains a finite subset B such that Gamma(B) = Gamma(S). This result was proved for k = 1,2 in an earlier paper, but the proof for k > 2 contained an error. (Author)