Algebraic entropy was introduced by Bellon and Viallet as a measure of complexity of algebraic systems. Having zero algebraic entropy is one of the forms of integrability in discrete case. I will discuss how looking for algebraic entropy leads to interesting questions and answers in two settings: that of bipartite T-systems, coming from the world cluster algebras, and that of R-systems, coming from the recently active area of dynamical algebraic combinatorics. In the case of T-systems this leads to a classification result related to classifying all pairs of commuting Cartan matrices of affine type. The talk is based on joint works with Pavel Galashin.
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