The Skew and Relative Derangements of Type $B$

  • William Y.C. Chen
  • Jessica C.Y. Zhang


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.

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