Inverse semigroup spectral analysis for partially ranked data

Martin E. Malandro

doi:10.1016/j.acha.2012.07.009

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arXiv · 1110.5679

Inverse semigroup spectral analysis for partially ranked data

Martin E. Malandro

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Abstract

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.

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BibTeX RIS

Martin E. Malandro. 2011-10-25. Inverse semigroup spectral analysis for partially ranked data. https://doi.org/10.1016/j.acha.2012.07.009

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