2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170379This 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 figuresCombinatoricsRepresentation Theory05A15; 05E05, 34C14, 11D45text