Bijective coding in the constructive world of R_c^n

Abstract

The methods of representation of structures in the standard cubic lattice Rnc in the form of bijective coding on a finite alphabet are developed. These methods are directed on an efficient computer implementation during the storage and computation of topological, metric and combinatorial performances of such structures for large values of n. The Hausdorff-Hamming metric for k-faces on an n-cube is extended to the Gromov-Hausdorff metric between «cubic» metric spaces. Simplicial partitions in an n-cube, their bijective coding, and ergodic properties are considered. Combinatorial filling at partitions on Rnc and related numerical performances are considered with respect to capabilities of supercomputers.