Geodesic
Symbolic computations in the lattice space $\mathbb{R}_{c}^{n}$
Numerical methods and programming, Tome 12 (2011) no. 4, pp. 409-416.

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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. 
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     author = {G. G. Ryabov and V. A. Serov},
     title = {Symbolic computations in the lattice space $\mathbb{R}_{c}^{n}$},
     journal = {Numerical methods and programming},
     pages = {409--416},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2011_12_4_a2/}
}
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G. G. Ryabov; V. A. Serov. Symbolic computations in the lattice space $\mathbb{R}_{c}^{n}$. Numerical methods and programming, Tome 12 (2011) no. 4, pp. 409-416. http://geodesic.mathdoc.fr/item/VMP_2011_12_4_a2/