Special Transpositions of Permutation Elements and Properties of Their Composition

@article{Grebennik2017SpecialTO,
  title={Special Transpositions of Permutation Elements and Properties of Their Composition},
  author={Igor V. Grebennik and Olena Chorna},
  journal={Cybernetics and Systems Analysis},
  year={2017},
  volume={53},
  pages={67-77}
}
We propose a strategy to solve the problem of optimization of a linear function on the set of cyclic permutations. The strategy is based on the properties of transpositions of special kind. The properties of this class of transpositions are investigated. Assertions about the impact of compositions of such transpositions on an arbitrary permutation are proved. For the approximate solutions obtained using the above strategy, estimation is substantiated.