  The Sliding Window Secretary Problem allows a window of choices to the
Classical Secretary Problem, in which there is the option to choose the
previous $K$ choices immediately prior to the current choice. We consider a
case of this sequential choice problem in which the interviewer has a finite,
known number of choices and can only discern the relative ranks of choices, and
in which every permutation of ranks is equally likely. We examine three cases
of the problem: (i) the interviewer has one choice to choose the best
applicant; (ii) the interviewer has one choice to choose one of the top two
applicants; and (iii) the interviewer has two choices to choose the best
applicant. The form of the optimal strategy is shown, the probability of
winning as a function of the window size is derived, and the limiting behavior
is discussed for all three cases.
