A d-move local permutation routing for the d-cube

On the coverings of the d-cube for d<=6

The cut number S(d) of the d-cube is the minimum number of hyperplanes in R that slice, that is cut the edges while avoiding vertices, all the edges of the d-cube. The cut number problem for the hypercube of dimensions d ≥ 4 was posed by P. O’Neil more than thirty years ago [17]. The identity S(3) = 3 is easy and that of S(4) = 4 is a well-known result, see [5,6,18]. However, the conjecture of ...

Large k-D Simplices in the d-Dimensional Cube

Automorphisms of the Cube n^d

Consider a hypergraph H d n where the vertices are points of the d-dimensional combinatorial cube n d and the edges are all sets of n points such that they are in one line. We study the structure of the group of automorphisms of H d n , i.e., permutations of points of n d preserving the edges. In this paper we provide a complete characterization. Moreover, we consider the Colored Cube Isomorphi...

Asymptotically efficient triangulations of the d-cube

Triangulating the regular d-cube I = [0, 1] in a “simple” way has many applications, like solving differential equations by finite element methods or calculating fixed points. See, for example, [7]. Determining the smallest number of simplices needed has brought special attention both from a theoretical point of view and from an applied one (see [6, Section 14.5.2] for a recent survey). Before ...

3 - D Hardcopy : The Hosoya Cube

Much effort in scientific visualization is put towards the representation and communication of three-dimensional objects. Typically, an investigator labors in front of a graphics workstation, twiddling knobs and flipping switches until meaningful views of the object are created. Once the investigator has found the correct representation of the data, the problem arises of how to communicate this...