Two new families of cluster Cohn and Markov-monodromy matrices for generalized Markov cluster algebras are introduced, fully classified, and made explicit via weighted fence posets whose order ideals expand cluster variables.
An elementary proof of uniqueness of Markoff numbers which are prime powers
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We present a very elementary proof of the uniqueness of Markoff numbers which are prime powers or twice prime powers, in the sense that it uses neither algebraic number theory nor hyperbolic geometry.
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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations
Two new families of cluster Cohn and Markov-monodromy matrices for generalized Markov cluster algebras are introduced, fully classified, and made explicit via weighted fence posets whose order ideals expand cluster variables.