منابع مشابه
Packing polyominoes clumsily
For a set D of polyominoes, a packing of the plane with D is a maximal set of copies of polyominoes from D that are not overlapping. A packing with smallest density is called a clumsy packing. We give an example of a set D such that any clumsy packing is aperiodic. In addition, we compute the smallest possible density of a clumsy packing when D consists of a single polyomino of a given size and...
متن کاملPolyominoes determined by involutions
A permutomino of size n is a polyomino determined by particular pairs (π1, π2) of permutations of length n, such that π1(i) 6= π2(i), for 1 ≤ i ≤ n. In this paper we consider the class of convex permutominoes which are symmetric with respect to the diagonal x = y. We determine the number of these permutominoes according to the dimension and we characterize the class of permutations associated t...
متن کاملEnumeration of generalized polyominoes
As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular k-gons. For n ≤ 4 we determine formulas for the number ak(n) of generalized polyominoes consisting of n regular k-gons. Additionally we give a table of the numbers ak(n) for small k and n obtained by computer enumeration. We finish with some open problems for k-polyominoes.
متن کاملClumsy packings with polyominoes
For a set D of polyominoes, a packing of the plane with D is a maximal set of copies of polyominoes from D that are not overlapping. A packing with smallest density is called clumsy packing. We give an example of a set D such that any clumsy packing is aperiodic. In addition, we compute the smallest possible density of a clumsy packing when D consist of a single polyomino of a given size and sh...
متن کاملPolyominoes determined by permutations
In the plane Z × Z a cell is a unit square, and a polyomino is a finite connected union of cells having no cut point. Polyominoes are defined up to translations. A column (row) of a polyomino is the intersection between the polyomino and an infinite strip of cells whose centers lie on a vertical (horizontal) line. The enumeration problem for general polyominoes is difficult to solve and still o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Geometry
سال: 2014
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2013.08.011