Folded bump diagrams for partitions of classical types

We introduce folded bump diagrams for BnBn, CnCn and DnDn partitions. They allow us to use the type A methods to handle all other classical types simultaneously. As applications, we give uniform interpretations for two families of bijections between noncrossing and nonnesting partitions, where the first family preserves openers and closers, while the second family preserves the statistics a and μ. Here a is the increasing sequence of the minimal elements of the blocks, and μ is the sizes of these blocks. We also extend the results of Chen, Deng, Du, Stanley and Yan (2007) [5] and Kasraoui and Zeng (2006) [10] concerning the symmetry of partitions of type A to other classical types uniformly.