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Elements transpositions and their impact on the cyclic structure of permutations

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The objective of this paper is the investigation of the cyclic structure and permutation properties based on neighbor elements transposition properties and the properties of the permutation polyhedron. In this paper we consider special type of transpositions of elements in a permutation. A feature of these transpositions is that they corresponding to the adjacency criterion in a permutation polyhedron. We will investigate permutation properties with the help of the permutation polyhedron by using the immersing in the Euclidian space. Six permutation types are considered in correspondence with the location of arbitraży components. We consider the impact of the corresponding components on the cyclic structure of permutations depending on the type of a permutation. In this paper we formulate the assertion about the features of the impact of transpositions corresponding to the adjacency criterion on the permutations consisting of the one cycle. During the proof of statement all six types of permutations are considered and clearly demonstrated that only two types arrangement of the elements in the cycle contribute to the persistence a single cycle in the permutation after the impast of two transpositions. Research conducted in the Niven work, will be further employed in mathematical modeling and computational methods. Especially for solving combinatorial optimization problems and for the generation of combinatorial objects with a predetermined cyclic structure.
Twórcy
autor
  • Kharkiv National University of Radio Electronics
autor
  • Kharkiv National University of Radio Electronics
Bibliografia
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  • 3. Grebennik.I., Pankratov.A., Chugay.A. and Baranov.A. 2010. Packing n-dimensional parallelepipeds with the feasibility of changing their orthogonal orientation in an n-dimensional parallelepiped. Cybernetics and Systems Analysis, 46(5), 793-802.
  • 4. Stanley R. 1986. Enumerative combinatorics, vol 1, Wadsworth, Inc. California.
  • 5. Stoyan Yu., Yemets О. 1993. Theory and methods of Euclidean combinatorial optimization, ISDO, Kyiv. (In Ukrainian)
  • 6. Grebennik I. V. 2010. Description and generation of permutations containing cycles. Cybernetics and Systems Analysis, 46(6), 97-105.
  • 7. Knuth Donald. 2005. The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations, Addison-Wesley, 144.
  • 8. Kreher Donald L., Stinson Douglas R. 1999. Combinatorial Algorithms: Generation Enumeration and Search, CRC Press, 329.
  • 9. Bona M. 2004. Combinatorics of Permutations, Chapman Hall-CRC, 383.
  • 10.Brualdi Richard A. 2010. Introductory Combinatorics, Fifth Edition, Pearson Education, 605.
  • 11.Bender Edward A., Williamson S.G. 2006. Foundations of Combinatorics with Applications, Dover, 468.
  • 12. Flajolet P., Sedgewick R. 2009. Analytic Combinatorics. Cambridge University Press, Cambridge, UK, 809.
  • 13. Stoyan Yu.G., Grebennik I. V. 2013. Description and Generation of Combinatorial Sets Having Special Characteristics. International Journal of Biomedical Soft Computing and Human Sciences, Special Volume “Bilevel Programming, Optimization Methods, and Applications to Economics” 18(1). 83-88
  • 14.Grebennik V., Lytvynenko O. S. 2012. Generation of combinatorial sets possessing special characteristics. Cybernetics and Systems Analysis, 48(6).
  • 15. Semenova N. V., Kolechkina L. N., Nagornaya A.N. 2008. Approach to solving the problems of vector discrete combinatorial optimization on a set of permutations. Cybernetics and Systems Analysis, 44(3).
  • 16. Semenova N. V., Kolechkina L. N. 2009. Polyhedral approach to solving a class of vector combinatorial optimization problems. Cybernetics and Systems Analysis, 45(3).
  • 17. Semenova N.V., Kolechkina L.N. 2009. Vector discrete optimization problems on combinatorial sets: Methods and resolution. K.: Naukova Dumka. (In Ukrainian)
  • 18. Isachenko Y.A. 2008. Application of polyhedral approach to the problem of cyclic permutations. Advanced computer information technology, YKSUG, vol 2, Grodno, 203-206. (In Russian)
  • 19. Grebennik I. V., Chorna О.S. 2014. Cyclic properties of adjacent permutations of different elements Bionics of intelligence, 1(82), 7–11.
  • 20. Alekseyev I., Khoma I., Shpak N. 2013. Modelling of an impact of investment maintenance on the condition of economic protectability of industrial enterprises. Econtechmod 2(2), Lublin ; Rzeszow, 3-8.
  • 21. Heorhiadi, Iwaszczuk N., Vilhutska R. 2013. Method of morphological analysis of enterprises management organizational structure. Econtechmod 2(4), Lublin; Rzeszow, 17-27.
  • 22. Podolchak N., Melnyk L., Chepil B. 2014. Improving administrative management costs Rusing optimization modeling. Econtechmod 3(1), Lublin; Rzeszow, 75–80.
  • 23. Lobozynska S. 2014. Formation of optimal model of regulation of the banking system of Ukraine. Econtechmod 3(2), Lublin; Rzeszow, 53-57.
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Bibliografia
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bwmeta1.element.baztech-9dedd29d-1383-4289-9acb-ee3a3c588a0b
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