Abstract
The aim of this paper is two-fold: (1) to introduce four systems of equations called M-systems and dual M-systems of types |$A_{n}$| and |$B_{n}$|, respectively; (2) to make a connection between M-systems (dual M-systems) and cluster algebras, and prove that the Hernandez–Leclerc conjecture is true for minimal affinizations of types |$A_n$| and |$B_n$|.
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