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Totally Positive Completable Matrix Patterns and Expansion

Allen, David
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.
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2019-05-01
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Undergraduate Honors Theses
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thesis_draft.pdf
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Johnson, Charles
Vinroot, Ryan
Kemper, Peter
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Mathematics
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https://scholarworks.wm.edu/handle/internal/10787
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