TILING WITH PUNCTURED INTERVALS
نویسندگان
چکیده
منابع مشابه
Tiling with Commutative Rings
so that every square is covered by exactly one domino? In other words, can R be tiled by vertical and horizontal dominoes? The coloring gives the answer to this well-known problem away. The region R has 32 black squares and 30 white squares. Since each domino covers exactly one black and one white square, no tiling is possible. The aim of this article is to explain a way to tackle tiling proble...
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We explore the complexity of tiling finite subsets of the plane, which we call layouts, with a finite set of tiles. The tiles are inspired by Wang tiles and the domino game piece. Each tile is composed of a pair of faces. Each face is colored with one of possible colors. We want to know if a given layout is tileable by a given set of dominoes. In a tiling, dominoes that touch must do so at like...
متن کاملTiling with Small Tiles
We look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems – we give an example of this. We also present a result to a more classic tiling question with dominoes and L-shape tiles.
متن کاملTiling Polyhedra with Tetrahedra
When solving an algorithmic problem involving a polyhedron in R, it is common to start by partitioning the given polyhedron into simplier ones. The most common process is called triangulation and it refers to partitioning a polyhedron into tetrahedra in a face-to-face manner. In this paper instead of triangulations we will consider tilings by tetrahedra. In a tiling the tetrahedra are not requi...
متن کاملTiling 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...
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ژورنال
عنوان ژورنال: Mathematika
سال: 2018
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579318000384