Enumeration and Generation of Permutations with a Partially Fixed Order of Elements

  • Yuri G. Stoyan Podgorny Institute for Mechanical Engineering Problems
  • Igor V. Grebennik Kharkiv National University of Radio Electronics
  • Viacheslav V. Kalashnikov Central Economics and Mathematics Institute (CEMI)
  • Oleksandr S. Lytvynenko Kharkiv National University of Radio Electronics
Keywords: Enumeration and Generation of Permutations, Partially Fixed Order of Elements

Abstract

A specific class of permutations – permutations with partially fixed order of elements – has been described. A procedure of enumeration and generation of this class has been developed. Steps of the algorithm have been established to be well-defined, and its complexity has been evaluated. Some important particular classes of permutations, such as alternating and unimodal ones are special cases of the permutations described. This algorithm can be used for generating other combinatorial sets, e.g. arrangements and combinations.

Published
2018-01-08
How to Cite
Stoyan, Y. G., Grebennik, I., Kalashnikov, V., & Lytvynenko, O. (2018). Enumeration and Generation of Permutations with a Partially Fixed Order of Elements. International Journal of Combinatorial Optimization Problems and Informatics, 8(1), 19-30. Retrieved from https://ijcopi.org/index.php/ojs/article/view/4
Section
Articles