Gray codes for noncrossing and nonnesting partitions of classical types

In this paper, we present Gray codes for the sets of noncrossing partitions associated with the classical Weyl groups, and for the set of nonnesting partitions of type B. An algorithm for the generation of type D nonnesting partitions is developed in which a Gray code is given for those partitions having a zero-block, while the remaining are arranged in lexicographic order