Minimally Intersecting Set Partitions of Type B

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 $B_n$-partitions, as well as a formula for the number of minimally intersecting r-tuples of $B_n$-partitions without zero-block. As a consequence, it follows the formula of Benoumhani for the Dowling number in analogy to Dobinski's formula.