The Skew and Relative Derangements of Type B
William Y.C. Chen and Jessica C.Y. Zhang
Abstract: By introducing the notion of relative derangements of type B, also called signed relative derangements, which are defined in terms of signed permutations, we obtain a type B analogue of the well-known relation between the relative derangements and the classical derangements. While this fact can be proved by using the principle of inclusion and exclusion, we present a combinatorial interpretation with the aid of the intermediate structure of signed skew derangements.
AMS Classification: 05E15, 05A05.
Keywords: signed permutations, relative derangement of type B, signed derangement, signed skew derangement.