Term of Award
Master of Science in Mathematics (M.S.)
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Thesis (open access)
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This work is licensed under a Creative Commons Attribution 4.0 License.
Department of Mathematical Sciences
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Packing patterns in words concerns finding a word with the maximum number of a prescribed pattern. The majority of the work done thus far is on packing patterns into permutations. In 2002, Albert, Atkinson, Handley, Holton and Stromquist showed that there always exists a layered permutation containing the maximum number of a layered pattern among all permutations of length n. Consequently, the packing density for all but two (up to equivalence) permutation patterns up to length 4 can be obtained. In this thesis we consider the analogous question for colored patterns and permutations. By introducing the concept of colored blocks we characterize the optimal permutations with the maximum number of a given colored pattern when it contains at most three colored blocks. As examples, we apply this characterization to find the optimal permutations of various colored patterns and subsequently obtain their corresponding packing densities.
Just, Matthew R., "Combinatorial Optimization of Subsequence Patterns in Words" (2016). Electronic Theses and Dissertations. 1464.
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