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A Study of Genetic Code by Combinatorics and Linear Algebra Approaches
Crowder, Tanner Jennings
Crowder, Tanner Jennings
Abstract
The genetic code-based matrices constructed in this work and the corresponding hamming distance matrices are studied using combinatorics and linear algebra approaches. Recursive schemes for generating the matrices are obtained. Algebraic properties such as ranks, eigenvalues, and eigenvectors of the Hamming distance matrices are examined. The results lead to an easy calculation of the powers of the Hamming distance matrices. Moreover, a decomposition of the Hamming Distance matrices in terms of permutation matrices is obtained. The decomposition gives rise to hypercube structures to the genetic code based matrices. A new scheme is given to generate matrices where each entry is a 4-tuple, which counts the number of each nucleotide in the entries of the genetic code matrix. Connections and potential applications of the results will be discussed.
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Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.
Date
2008-05-16
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Keywords
Genetic Code, Hamming Distance, Gray Code, Eigenstructure
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Department
Mathematics