  Motivated by the notion of symmetric group spectral analysis developed by
Diaconis, we introduce the notion of spectral analysis on the rook monoid (also
called the symmetric inverse semigroup), characterize its output in terms of
symmetric group spectral analysis, and provide an application to the
statistical analysis of partially ranked (voting) data. We also discuss
generalizations to arbitrary finite inverse semigroups. This paper marks the
first non-group semigroup development of spectral analysis.
