Graduation Year
2014
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Michael Orrison
Reader 2
Mohamed Omar
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
Rights Information
© 2014 Matthew McDermott
Abstract
Imagine your local creamery administers a survey asking their patrons to choose their five favorite ice cream flavors. Any data collected by this survey would be an example of partially ranked data, as the set of all possible flavors is only ranked into subsets of the chosen flavors and the non-chosen flavors. If the creamery asks you to help analyze this data, what approaches could you take? One approach is to use the natural symmetries of the underlying data space to decompose any data set into smaller parts that can be more easily understood. In this work, I describe how to use permutation representations of the symmetric group to create and study efficient algorithms that yield such decompositions.
Recommended Citation
McDermott, Matthew, "Fast Algorithms for Analyzing Partially Ranked Data" (2014). HMC Senior Theses. 58.
https://scholarship.claremont.edu/hmc_theses/58
Source Fulltext
http://www.math.hmc.edu/~mmcdermott/thesis/mmcdermott-2014-thesis.pdf
Included in
Algebra Commons, Harmonic Analysis and Representation Commons, Other Applied Mathematics Commons, Theory and Algorithms Commons
