Date Thesis Awarded
5-2019
Access Type
Honors Thesis -- Access Restricted On-Campus Only
Degree Name
Bachelors of Science (BS)
Department
Mathematics
Advisor
Charles Johnson
Committee Members
Ryan Vinroot
Peter Kemper
Abstract
Though some special cases are now understood, the characterization of TP-completable patterns is far from complete. Here, a new idea is developed: the \underline{expansion} of a pattern. It is used to explain some recent results, such as border patterns. The effects of expansion on certain cases of non-completable and completable patterns is examined, as well as an attempt to characterize $3$-by-$n$ TP-completable patterns. While many TP-completable patterns remain so under expansion, a counterExample shows that this is not always so. In the process, some new results about TP-completability are given.
Recommended Citation
Allen, David, "Totally Positive Completable Matrix Patterns and Expansion" (2019). Undergraduate Honors Theses. William & Mary. Paper 1388.
https://scholarworks.wm.edu/honorstheses/1388
