Вычислительные методы и приложения

Symbolic computations in the lattice space $\mathbb{R}_{c}^{n}$

G. G. Ryabov, V. A. Serov

M.V. Lomonosov Moscow State University, Research Computing Center

Abstract: The methods of cubic structure coding for an $n$-cube and a cubic $n$-neighborhood in the lattice space $\mathbb{R}_{c}^{n}$ are developed in a more general context of the language formalism. The choice of an alphabet and its relation to the above problems on cubic structures for a cubic $n$-neighborhood of radius $r$ ($r$ is integer) are considered with the aim of computer constructing of cubic structures and manifolds with prescribed properties. The mapping of subsets of the set $\mathbb{Z}$ onto the finite Hausdorff metric spaces whose points are all $k$-dimensional faces of an $n$-cube is analyzed. The efficiency of symbolic computations is discussed in the context of computer implementation. This work was supported by the Russian Foundation for Basic Research (project no. 09-07-12135-ofi_m).

Keywords: lattice space $\mathbb{R}_{c}^{n}$; representations of $k$-faces in $n$-cube; Hausdorff–Hamming metrics; symbolic operations.

UDC: 512.531; 515.124; 004.2