Some conjectures on generalized cluster algebras via the cluster formula and $D$-matrix pattern

Abstract

In the theory of generalized cluster algebras, we build the so-called cluster formula and $D$-matrix pattern. Then as applications, some fundamental conjectures of generalized cluster algebras are solved affirmatively.

16 pages

References in corpus (3)

• Exact WKB analysis and cluster algebras II: Simple poles, orbifold points, and generalized cluster algebras
• Structure of seeds in generalized cluster algebras
• Quantum affine algebras at roots of unity and generalised cluster algebras