Date Thesis Awarded

5-2019

Document Type

Honors Thesis

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.

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