Summary
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.
Mathematics Subject Classifications (2010). 20M99, 90C10
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Labrousse, D., Alfonsín, J.L.R. (2010). A Tiling Problem and the Frobenius Number. In: Chudnovsky, D., Chudnovsky, G. (eds) Additive Number Theory. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68361-4_15
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DOI: https://doi.org/10.1007/978-0-387-68361-4_15
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