Singletons and Adjacencies of Set Partitions of Type B
William Y.C. Chen and David G.L. Wang
Abstract: We show that the joint distribution of the number of singleton pairs and the number of adjacency pairs is symmetric over the set partitions of type Bn without zero-block, in analogy with the result of Callan for ordinary partitions.
AMS Classification: 05A15, 05A18, 20F55
Keywords: set partition of type B, singleton, adjacency, symmetric distributions