منابع مشابه
Polyboxes, Cube Tilings and Rigidity
A non-empty subset A of X = X1 × · · · × Xd is a (proper) box if A = A1 × · · · × Ad and Ai ⊂ Xi for each i. Suppose that for each pair of boxes A, B and each i, one can only know which of the three states takes place: Ai = Bi, Ai = Xi \ Bi, Ai 6∈ {Bi, Xi \ Bi}. Let F and G be two systems of disjoint boxes. Can one decide whether ⋃ F = ⋃ G ? In general, the answer is ‘no’, but as is shown in th...
متن کاملThe Multidimensional Cube Recurrence
We introduce a recurrence which we term the multidimensional cube recurrence, generalizing the octahedron recurrence studied by Propp, Fomin and Zelevinsky, Speyer, and Fock and Goncharov and the three-dimensional cube recurrence studied by Fomin and Zelevinsky, and Carroll and Speyer. The states of this recurrence are indexed by tilings of a polygon with rhombi, and the variables in the recurr...
متن کاملCube Tilings of R and Nonlinear Codes
Families of non-lattice tilings of R by unit cubes are constructed. These tilings are specializations of certain families of nonlinear codes over GF( 2 ). These cube-tilings provide building blocks for the construction of cube-tilings such that no two cubes have a high-dimensional face in common. We construct cube-tilings of R such that no two cubes have a common face of dimension exceeding n −...
متن کاملCube-Tilings of Rn and Nonlinear Codes
Families of non-lattice tilings of R n by unit cubes are constructed. These tilings are specializations of certain families of nonlinear codes over GF( 2 ). These cube-tilings provide building blocks for the construction of cube-tilings such that no two cubes have a high-dimensional face in common. We construct cube-tilings of R n such that no two cubes have a common face of dimension exceeding...
متن کاملThe Hyper-Panconnectedness of the Crossed Cube
A connected graph G is said to be panconnected if, for any two distinct vertices x and y of G, it contains a path P between x and y such that dP(x, y) = l for any integer l satisfying dG(x, y) l |V(G)| – 1, where dG(x, y) (respectively, dP(x, y)) denotes the distance between x and y in G (respectively, P), and |V(G)| denotes the total number of vertices of G. If such path P can be extended ...
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: Acta Crystallographica Section A Foundations and Advances
سال: 2018
ISSN: 2053-2733
DOI: 10.1107/s2053273318090186