Description and generation of permutations containing cycles

Abstract

The paper proposes a general approach to generating permutations that contain cycles, based on constructive tools introduced to describe combinatorial sets. Different generation problems for permutations of definite class are formulated and solved. A combinatorial set is introduced to define permutations represented as the multiplication of a definite number of cycles. For this set, combinatorial species and associated generating series are constructed.

Solution Strategy for One-to-One Pickup and Delivery Problem Using the Cyclic Transfer Approach

“…The solution of the problem (6) depends on the properties of the set of cyclic permutations that are studied in [51], [52]. Solution algorithms of the problem (6) are developed in [53] for the linear function…”