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 OJDM  Vol.6 No.2 , April 2016
Algebra and Geometry of Sets in Boolean Space
Vladimir Leontiev1, Garib Movsisyan2*, Zhirayr Margaryan3
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Abstract: In the present paper, geometry of the Boolean space Bn in terms of Hausdorff distances between subsets and subset sums is investigated. The main results are the algebraic and analytical expressions for representing of classical figures in Bn and the functions of distances between them. In particular, equations in sets are considered and their interpretations in combinatory terms are given.
Keywords: Equations on Sets, Hausdorff Distance, Hamming Distance, Generating Function, Minkowski Sum, Sum of Sets
Cite this paper: Leontiev, V. , Movsisyan, G. and Margaryan, Z. (2016) Algebra and Geometry of Sets in Boolean Space. Open Journal of Discrete Mathematics, 6, 25-40. doi: 10.4236/ojdm.2016.62004.
References

[1]   Nigmatulin, R.G. (1991) Complexity of Boolean Functions. Moscow, Nauka, 240 (in Russian).

[2]   McWilliams, F.J. and Sloane, N.J.A. (1977) The Theory of Error-Correcting Codes, Parts I and II. North-Holland Publishing Company, Amsterdam.

[3]   Leontiev, V.K. (2001) Selected Problems of Combinatorial Analysis. Bauman Moscow State Technical University, Moscow, 2001 (in Russian).

[4]   Leontiev, V.K. (2015) Combinatorics and Information. Moscow Institute of Physics and Technology (MIPT), Moscow, 2015 (in Russian).

[5]   Leontiev, V.K., Movsisyan, G.L. and Osipyan, A.A. (2014) Classification of the Subsets Bn, and the Additive Channels. Open Journal of Discrete Mathematics (OJDM), 4, 67-76.

[6]   Leontiev, V.K., Movsisyan, G.L., Osipyan, A.A. and Margaryan, Zh.G. (2014) On the Matrix and Additive Communication Channels. Journal of Information Security (JIS), 5, 178-191.

[7]   Leontiev, V.K., Movsisyan, G.L. and Margaryan, Zh.G. (2012) Constant Weight Perfect and D-Representable Codes. Proceedings of the Yerevan State University, Physical and Mathematical Sciences, 16-19.

[8]   Movsisyan, G.L. (1982) Perfect Codes in the Schemes Johnson. Bulletin of MSY, Computing Mathematics and Cybernetics, 1, 64-69 (in Russian).

[9]   Movsisyan, G.L. (2013) Dirichlet Regions and Perfect Codes in Additive Channel. Open Journal of Discrete Mathematics (OJDM), 3, 137-142.

 
 
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