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.
متن کاملLattice Tilings by Cubes: Whole, Notched and Extended
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...
متن کاملAn Efficient Strategy for Tiling Multidimensional OLAP Data Cubes
Computing aggregates over selected categories of multidimensional discrete data (MDD) cubes is the core operation of many on-line analytical processing (OLAP) systems. In order to support efficient computations of these aggregates in a multidimensional OLAP (MOLAP) system, a careful design of the database storage architecture must be undertaken. In particular, tiling (i.e., subdivision of an MD...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00310-6