%0 Journal Article %T Invariants, Kronecker Products, and Combinatorics of Some Remarkable Diophantine Systems (Extended Version) %A Adriano Garsia %A Gregg Musiker %A Nolan Wallach %A Guoce Xin %J Mathematics %D 2008 %I arXiv %X 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. %U http://arxiv.org/abs/0810.0060v1