منابع مشابه
Rhombus Tilings of a Hexagon with Three Fixed Border Tiles
Abstract. We compute the number of rhombus tilings of a hexagon with sides a+2, b+2, c+2, a+ 2, b+2, c+2 with three fixed tiles touching the border. The particular case a = b = c solves a problem posed by Propp. Our result can also be viewed as the enumeration of plane partitions having a + 2 rows and b + 2 columns, with largest entry ≤ c + 2, with a given number of entries c + 2 in the first r...
متن کاملSome New Tilings of the Sphere with Congruent Triangles
Many years ago, Sommerville classified the tilings of the sphere with congruent spherical triangles – under some assumptions. Later, Davies did the same, under only the restriction that the triangles should meet edge-to-edge. This paper surveys a recently-discovered class of tilings with congruent spherical triangle tiles that do not meet edgeto-edge. Introduction. Any simple polyhedron can be ...
متن کاملNeighbours of Self–Affine Tiles in Lattice Tilings
Let T be a tile of a self-affine lattice tiling. We give an algorithm that allows to determine all neighbours of T in the tiling. This can be used to characterize the sets VL of points, where T meets L other tiles. Our algorithm generalizes an algorithm of the authors which was applicable only to a special class of self-affine lattice tilings. This new algorithm can also be applied to classes c...
متن کاملIntegral Self Affine Tiles in R Ii Lattice Tilings
Let A be an expanding n n integer matrix with j det A j m A standard digit set D for A is any complete set of coset representatives for Z A Z Associated to a given D is a set T A D which is the attractor of an a ne iterated function system satisfying T d D T d It is known that T A D tiles R n by some subset of Z This paper proves that every standard digit set D gives a set T A D which tiles R w...
متن کاملON ONE - DIMENSIONAL SELF - SIMILAR TILINGS AND pq - TILES
Let b ≥ 2 be an integer base, D = {0, d1, · · · , db−1} ⊂ Z a digit set and T = T (b,D) the set of radix expansions. It is well known that if T has nonvoid interior, then T can tile R with some translation set J (T is called a tile and D a tile digit set). There are two fundamental questions studied in the literature: (i) describe the structure of J ; (ii) for a given b, characterize D so that ...
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: Bulletin of the American Mathematical Society
سال: 1980
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1980-14827-2