Derangements and Relative Derangements of Type $B$

Details Derangements and Relative Derangements of Type $B$ Derangements and Relative Derangements of Type $B$

2007-08-27

arxiv.org/abs/0708.3623v1

Mathematics

Combinatorics

7 pages

Scientific paper

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 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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