  A conjecture by R. Stanley on a class of alternating permutations, which is
proved by R. Chapman and L. Williams states that alternating permutations with
the maximal number of fixed points is equidistributed with derangements. We
extend this (type $A$) result to type $B$: We prove that various classes of
alternating signed permutations with the maximal number of fixed points is
equidistributed with certain types of derangements (of type $B$), respectively.
