Symbolic computations in the lattice space Rnc
Keywords:
lattice space Rnc, representations of k-faces in n-cube, Hausdorff-Hamming metrics, symbolic operationsAbstract
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).
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