Minimally Intersecting Set Partitions of Type B

William Y.C. Chen and David G.L. Wang

  Abstract:  Motivated by Pittel's study of minimally intersecting set partitions, we investigate minimally intersecting set partitions of type B. We find a formula for the number of minimally intersecting r-tuples of Bn-partitions, as well as a formula for the number of minimally intersecting r-tuples of Bn-partitions without zeroblock. As a consequence, it follows the formula of Benoumhani for the Dowling number in analogy to Dobinski's formula.

  AMS Classification:  05A15, 05A18

  Keywords:  minimally intersecting Bn-partitions, Dobinski's formula, the Dowling number.

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