A combinatorial approach to derangement matrix of type B

In this paper we extend the notion of type B derangements in two ways. First, we refine this notion by studying type B derangements when the number of cycles is fixed. Second, we introduce type B permutations when the number of colors applied to the elements is not necessarily two. We use generating functions, combinatorial arguments and Riordan arrays to study the combinatorial matrices associated to these derangements.