Tiling with polyominoes and combinatorial group theory
نویسندگان
چکیده
منابع مشابه
Tiling with polyominoes and combinatorial group theory
When can a given finite region consisting of cells in a regular lattice (triangular, square, or hexagonal) in [w’ be perfectly tiled by tiles drawn from a finite set of tile shapes? This paper gives necessary conditions for the existence of such tilings using boundary inuariants, which are combinatorial group-theoretic invariants associated to the boundaries of the tile shapes and the regions t...
متن کاملTiling a Rectangle with Polyominoes
A polycube in dimension d is a finite union of unit d-cubes whose vertices are on knots of the lattice Zd . We show that, for each family of polycubes E, there exists a finite set F of bricks (parallelepiped rectangles) such that the bricks which can be tiled by E are exactly the bricks which can be tiled by F . Consequently, if we know the set F , then we have an algorithm to decide in polynom...
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متن کاملKlarner systems and tiling boxes with polyominoes
Let T be a protoset of d-dimensional polyominoes. Which boxes (rectangular parallelepipeds) can be tiled by T ? A nice result of Klarner and Göbel asserts that the answer to this question can always be given in a particularly simple form, namely, by giving a finite list of “prime” boxes. All other boxes that can be tiled can be deduced from these prime boxes. We give a new, simpler proof of thi...
متن کاملTiling a Square with Eight Congruent Polyominoes
The problem of finding polyominoes that tile rectangles has attracted a lot of attention; see [1] for an overview, and [2, 3] for more recent results. Several general families of such polyominoes are known, but sporadic examples seem to be scarce. Marshall [2, Fig. 9] gives a polyomino of rectangular order 8, and asks if it can be generalized to a family of rectifiable polyominoes. Here we show...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1990
ISSN: 0097-3165
DOI: 10.1016/0097-3165(90)90057-4