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On the monotonicity of the generalized Markov numbers
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Using the Markov distance and Ptolemy inequality introduced by Lee-Li-Rabideau-Schiffler \cite{LLRS}, we completely determine the monotonicity of the generalized Markov numbers along the lines of a given slope.
Forward citations
Cited by 2 Pith papers
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Mutation-preserving generalized cluster algebras and Laurent mutation invariants
A new stability condition for generalized cluster algebras is classified, a Markov-type Diophantine equation is solved with explicit orbit counts, and the Chen-Li conjecture on rank-3 Laurent mutation invariants is proved.
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A cluster theory approach from mutation invariants to Diophantine equations
A cluster-mutation argument claims the Diophantine equation x1^2+x2^4+x3^4+2x1x2^2+2x1x3^2 = k x1 x2^2 x3^2 has positive integer solutions only for k=7, alongside a classification of sign-equivalent exchange matrices.
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