"Symbolic computations in the lattice space R nc "
Ryabov G.G., Serov V.A.

The methods of cubic structure coding for an n-cube and a cubic n-neighborhood in the lattice space Rnc 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 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 Rnc, representations of k-faces in n-cube, Hausdorff-Hamming metrics, symbolic operations

Ryabov G.G.   e-mail: gen-ryabov@yandex.ru;   Serov V.A.   e-mail: v_serov_@mail.ru