Tiling space with notched cubes
نویسندگان
چکیده
منابع مشابه
Tiling with notched cubes
In 1966, Golomb showed that any polyomino which tiles a rectangle also tiles a larger copy of itself. Although there is no compelling reason to expect the converse to be true, no counterexamples are known. In 3 dimensions, the analogous result is that any polycube that tiles a box also tiles a larger copy of itself. In this note, we exhibit a polycube (a ‘notched cube’) that tiles a larger copy...
متن کاملTiling space with notched
Stein (1990) discovered (n l)! lattice tilings of R” by translates of the notched n-cube which are inequivalent under translation. We show that there are no other inequivalent tilings of IF!” by translates of the notched cube.
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We discuss some problems of lattice tiling via Harmonic Analysis methods. We consider lattice tilings of R by the unit cube in relation to the Minkowski Conjecture (now a theorem of Hajós) and give a new equivalent form of Hajós’s theorem. We also consider “notched cubes” (a cube from which a reactangle has been removed from one of the corners) and show that they admit lattice tilings. This has...
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A rep-tiling ~is a self replicating, lattice tiling of R". Lattice tiling means a tiling by translates of a single compact tile by the points of a lattice, and self-replicating means that there is a non-singular linear map ¢: R"-o R" such that, for each T e J, the image 4~(T) is, in turn, tiled by Y-. This topic has recently come under investigation, not only because of its recreational appeal,...
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Recently there has been some interest in the combinatorics of the geometry of the Hamming space, e.g., [10], and in particular, in tilings of this space [8]. Here, we investigate partitions of the Hamming space into spheres with possibly different radii. Such a partition is sometimes called a generalized perfect code, see e.g. [1, 3, 6, 13, 15]. Generalized spherepacking bounds can be found in ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90029-9