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 Vychisl. Metody Programm., 2011, Volume 12, Issue 4, Pages 409–416 (Mi vmp209)

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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

Full text: PDF file (327 kB)
UDC: 512.531; 515.124; 004.2

Citation: G. G. Ryabov, V. A. Serov, “Symbolic computations in the lattice space $\mathbb{R}_{c}^{n}$”, Vychisl. Metody Programm., 12:4 (2011), 409–416

Citation in format AMSBIB
\Bibitem{RyaSer11} \by G.~G.~Ryabov, V.~A.~Serov \paper Symbolic computations in the lattice space $\mathbb{R}_{c}^{n}$ \jour Vychisl. Metody Programm. \yr 2011 \vol 12 \issue 4 \pages 409--416 \mathnet{http://mi.mathnet.ru/vmp209}