The A-infinity T-system, also known as the octahedron recurrence, is a three-dimensional recurrence that originally arose in the context of Dodgson condensation, a method for iteratively computing the determinant of a matrix. The octahedron recurrence has received a great deal of attention over the past 25 years. As a consequence of cluster algebra theory, one can express the terms in this recurrence as Laurent polynomials in initial conditions. In this talk, we discuss the combinatorics of solutions of T-systems, including Speyer's bijection of the terms of these Laurent polynomials with perfect matchings of the Aztec diamond. No background in cluster algebras will be expected. Speaker(s): Alexander Leaf (University of Michigan)