منابع مشابه
Winning Strategies for Hexagonal Polyomino Achievement
In polyomino achievement games, two players alternately mark the cells of a tessellation and try to achieve a given polyomino. In [2], Bode and Harborth investigated polyomino achievement games for the hexagonal tessellation and determined all but five polyominoes with at most five cells whether they are achieved by the first player. In this paper, we show winning strategies for three hexagonal...
متن کاملRectangular polyomino set weak (1, 2)-achievement games
In a polyomino set (1,2)-achievement game the maker and the breaker alternately mark one and two previously unmarked cells respectively. The maker's goal is to mark a set of cells congruent to one of a given set of polyominoes. The breaker tries to prevent the maker from achieving his goal. The teams of polyominoes for which the maker has a winning strategy is determined up to size 4. In set ac...
متن کاملCombinatorially Regular Polyomino Tilings
Let T be a regular tiling of R which has the origin 0 as a vertex, and suppose that φ : R → R is a homeomorphism such that i) φ(0) = 0, ii) the image under φ of each tile of T is a union of tiles of T , and iii) the images under φ of any two tiles of T are equivalent by an orientation-preserving isometry which takes vertices to vertices. It is proved here that there is a subset Λ of the vertice...
متن کاملPolyomino-Based Digital Halftoning
In this work, we present a new method for generating a threshold structure. This kind of structure can be advantageously used in various halftoning algorithms such as clustered-dot or dispersed-dot dithering, error diffusion with threshold modulation, etc. The proposed method is based on rectifiable polyominoes -a non-periodic hierarchical structure, which tiles the Euclidean plane with no gaps...
متن کاملMinimum Area Polyomino Venn Diagrams
Polyomino Venn (or polyVenn) diagrams are Venn diagrams whose curves are the perimeters of polyominoes drawn on the integer lattice. Minimum area polyVenn diagrams are those in which each of the 2n intersection regions, in a diagram of n polyominoes, consists of exactly one unit square. We construct minimum area polyVenn diagrams in bounding rectangles of size 2r×2c whenever r, c ≥ 2. Our const...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00204-6