A Tiling Problem and the Frobenius Number

  • D. Labrousse
  • J. L. Ramírez Alfonsín


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.


Frobenius number Rectangle Tiling Torus 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • D. Labrousse
    • 1
  • J. L. Ramírez Alfonsín
    • 1
    • 2
  1. 1.Equipe Combinatoire et OptimisationUniversité Pierre et Marie Curie, Paris 6Paris Cedex 05France
  2. 2.Institut de Mathématiques et de Modelisation de MontpellierUniversité Montpellier 2MontpellierFrance

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