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.

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