METHOD OF SETTING THE RULES OF MATRIX CONFIGURATIONS ELEMENTS INDEXING
https://doi.org/10.21822/2073-6185-2016-42-3-101-109
Abstract
Aim. Develop a way to define the rules of indexing elements of combinatorial matrix configurations.
Methods. Introduced are the proposed rules use examples during elements permutation of matrix combinatorial configurations defined are families of derived configurations, formed by the individual elements, provided the element location in each possible positions of the configuration, determined is the number of possible configurations forming variants with the specified index environment, forming separate families.
Results. This article provides a method of setting the rules combinatorial matrix configurations elements indexing in the form of functional indices dependencies of environment elements of an element in the configuration from element indices, considered as a «central». A general view of the functional dependence of the index of elements surrounding the indices of any configuration item, regarded as a «central» is presented. The concept of elements «index remoteness» and the index remoteness coefficient, defined are the limits of its values.
Conclusion. Permutations a predetermined environment indexing element may be considered as basic combinatorial configuration with which the reading of data by various algorithms can be arranged: in rows, in columns, in a deterministic or random routes that provides an additional increase in resistance disclosure.
Keywords
indexing elements of combinatorial configurations,
index the environment of the elements,
the coefficient of the index of remoteness of the elements of the environment,
permutation of the elements of the matrix of combinatorial configurations with a given indexing environment,
properties and family configurations
About the Authors
I. P. Kadiev1
National Bank of the Republic of Dagestan of the Russian Federation Central Bank
Russian Federation
Russian Federation
leading specialist in the field of information protection of information-analytical Department of management of inspection of commercial organizations,
29. Daniyalov Str., Makhachkala, 36700
P. A. Kadiev
Daghestan State Technical University
Russian Federation
Russian Federation
candidate of technical Science, Professor of the Department of Informatics in technical systems,
70 I. Shamil Ave, Makhachkala, 367015
References
1. Reinhold E., Nivergelt Yu, Deo N. Combinatorial algorithms. Theory and practice. – Moscow: Mir. 1980, 476 p. (In Russian)
2. Chebrakov Y. The theory of magic squares. St. Petersburg: St. Petersburg. Gosudarstvennyj tehnicheskij universitet, 2008, 367p. (In Russian)
3. Electronic resource http:pmpu.ru/vf4/algebra2:cyclic(In Russian)
4. Anderson James. Discrete mathematics and combinatorics = Discrete Mathematics with Combinatorics. Moscow: Vil'jams, 2006, p.960.
5. Erosh IL Discrete Mathematics. Combinatorics. St. Petersburg: SPbGUAP, 2001, 374 p. (In Russian)
6. Stanley R. Combinatorial Enumeration. The trees, generating functions and symmetric functions = Enumerative Combinatorics. vol. 2. Moscow: Mir, 2009, pp.767.15.
7. Kadiev I.P., Kadiev P.A. About one class of combinatory configurations. Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskie nauki [Herald of Daghestan State Technical University. Technical science]. 2013, vol.31, no.4, pp.45-49. (In Russian) DOI:10.21822/2073-6185-2013-31-4-45-49
8. Kadiev I.P., Kadiev P.A. Cyclical methods of sorting the index elements datasets. Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskie nauki [Herald of Daghestan State Technical University. Technical science.]. 2015, vol. 36, no.1, pp.79-83. (In Russian) DOI:10.21822/2073-6185-2015-36-1-79-83
9. Kadiev P.A., Kadiev P.I., Mirzabekov T.M. The software package for data stream scrambling. Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskie nauki [Herald of Daghestan State Technical University. Technical science.]. 2016, vol.41, no.2, pp.83-93. (In Russian) DOI:10.21822/2073-6185-2016-41-2-83-93
10. Crapo H., Senato D. Algebvaic Combinatovics and Computer Sience, Springen, 2006, pp. 320-379.
11. Mark Jerrum, Alistair Sinclair and Eric Vigoda. A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries, J. ACM, 2004, vol.51, no.4, pp.671-697.
12. Roswitha Blind, Peter Mani-Levitska. Puzzles and polytope isomorphisms. Aequationes Mathematicae. 1987б, vol.34, no.2-3, pp.287–297. DOI:10.1007/BF01830678
13. Cook William, Paul D. Seymour. Polyhedral Combinatorics. American Mathematical Society. 1989, (DIMACS Series in Discrete Mathematics and Theoretical Computer Science), pp.120-146.
14. Francisco Santos Leal. A counterexample to the Hirsch conjecture. Annals of Mathematics. Princeton University and Institute for Advanced Study, 2011, vol.176, no.1, pp. 383–412 DOI:10.4007/annals.2012.176.1.7.
15. Gil Kalai. A simple way to tell a simple polytope from its graph. Journal of Combinatorial Theory. 1988, vol.49, no.2, pp.381–383. DOI:10.1016/0097-3165(88)90064-7.
Review
For citations:
Kadiev1 I.P., Kadiev P.A. METHOD OF SETTING THE RULES OF MATRIX CONFIGURATIONS ELEMENTS INDEXING. Herald of Dagestan State Technical University. Technical Sciences. 2016;42(3):101-109. (In Russ.) https://doi.org/10.21822/2073-6185-2016-42-3-101-109
Views:
573
Email this article 
