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On the monotonicity of the generalized Markov numbers

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arxiv 2204.11443 v2 pith:IA55AXYJ submitted 2022-04-25 math.NT math.CO

On the monotonicity of the generalized Markov numbers

classification math.NT math.CO
keywords markovgeneralizedmonotonicitynumbersalongcitecompletelydetermine
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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.

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  1. Orderings of Generalized k-Markov Numbers

    math.NT 2026-04 unverdicted novelty 6.0

    Generalized k-Markov numbers grow monotonically along more random lines as k increases, supporting a k-analog of Frobenius' uniqueness conjecture.