Hypercube – Simple English Wikipedia, the free encyclopedia, Hypercube – Wikipedia, Hypercube – Wikipedia, Latin squares can be generalized to d-dimensional hypercubes. For d ? 2, a d-dimensional hypercube of order q is a q × … × q array with q d points based upon q distinct symbols. For 0 ? i ? d ? 1, such a hypercube has type i if, whenever any i of the coordinates are fixed, each of the q symbols appears q d ? i ? 1 times in that subarray.
d {displaystyle d} -dimensional hypercube is a network topology for parallel computers with 2 d {displaystyle 2^{d}} processing elements. The topology allows for an efficient implementation of some basic communication primitives such as Broadcast, All-Reduce, and Prefix sum. The processing elements are numbered 0 {displaystyle 0} through 2 d ? 1 {displaystyle 2^{d}-1}. Each processing element is.
This can be generalized to any number of dimensions. This process of sweeping out volumes can be formalized mathematically as a Minkowski sum: the d-dimensional hypercube is the Minkowski sum of d mutually perpendicular unit-length line segments, and is therefore an example of a zonotope. The 1-skeleton of a hypercube is a hypercube graph.
Consider a d-dimensional problem of N zero-spin bosons in a d-dimensional hypercube with the side L and the hypervolume V = L d. For d = 1, this hypercube is just a line segment of length L; for d = 2, it is a square of area L 2, and for d = 3, it is an ordinary three-dimensional cube of the volume L 3. Let n = N/V denote the particle number …
Four-dimensional Space, Cube, Simplex, Five-dimensional Space, N-sphere
