English

Inverse semigroup spectral analysis for partially ranked data

Statistics Theory 2012-08-06 v3 Group Theory Representation Theory Statistics Theory

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.

Keywords

Cite

@article{arxiv.1110.5679,
  title  = {Inverse semigroup spectral analysis for partially ranked data},
  author = {Martin E. Malandro},
  journal= {arXiv preprint arXiv:1110.5679},
  year   = {2012}
}

Comments

v3: Significant changes in terms of organization and presentation. Accepted for publication in Appl. Comput. Harmon. Anal. 25 pages, 5 tables. v2: Some reformatting, minor typos corrected

R2 v1 2026-06-21T19:25:43.931Z