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

TL;DR

This paper explores the connections between invariants, Kronecker products, and combinatorics of Diophantine systems, revealing a unifying formal power series that advances understanding in quantum computing and related fields.

Contribution

It introduces a novel link via a formal power series connecting invariants, Kronecker products, and Diophantine combinatorics, providing new methods for solving related numerical problems.

Findings

Established a formal power series linking the three areas

Developed methods for solving numerical problems in each area

Provided new insights into the combinatorics of Diophantine systems

Abstract

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.