A tiling problem and the frobenius number

Abstract

In this paper, we investigate tilings of tori and rectangles with rectangular tiles. We present necessary and sufficient conditions for the existence of an integer C such that any torus, having dimensions greater than C, is tiled with two given rectangles (C depending on the dimensions of the tiles). We also give sufficient conditions to tile a sufficiently large n-dimensional rectangle with a set of (n-dimensional) rectangular tiles. We do this by combining the periodicity of some particular tilings and results concerning the so-called Frobenius number. © 2010 Springer Science+Business Media, LLC.