Invariants, Kronecker Products, and Combinatorics of Some Remarkable Diophantine Systems (Extended Version)

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This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single formal power series with a multifaced interpretation. The deeper exploration of this link yielded results as well as methods for solving some numerical problems in each of these separate areas.
33 pages, 5 figures

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