Inverse semigroup spectral analysis for partially ranked data

Details Inverse semigroup spectral analysis for partially ranked data Inverse semigroup spectral analysis for partially ranked data

2011-10-25

arxiv.org/abs/1110.5679v2

Mathematics

Statistics Theory

v2: Some reformatting, minor typos corrected. 34 pages, 23 tables

Scientific paper

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 inverse semigroups in general. This paper marks the first non-group semigroup development of spectral analysis.

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