Enumeration And Generation Of Permutations With A Partially Fixed Order Of Elements

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.