Minimally Intersecting Set Partitions of Type $B$

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


Motivated by Pittel's study of minimally intersecting set partitions, we investigate minimally intersecting set partitions of type $B$. Our main result is a formula for the number of minimally intersecting $r$-tuples of $B_n$-partitions. As a consequence, it implies the formula of Benoumhani for the Dowling number in analogy to Dobiński's formula.

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