# On the ordering of the Markov numbers

@article{Lee2020OnTO, title={On the ordering of the Markov numbers}, author={Kyungyong Lee and Li Li and Michelle Rabideau and Ralf Schiffler}, journal={arXiv: Number Theory}, year={2020} }

The Markov numbers are the positive integers that appear in the solutions of the equation $x^2+y^2+z^2=3xyz$. These numbers are a classical subject in number theory and have important ramifications in hyperbolic geometry, algebraic geometry and combinatorics.
It is known that the Markov numbers can be labeled by the lattice points $(q,p)$ in the first quadrant and below the diagonal whose coordinates are coprime. In this paper, we consider the following question. Given two lattice points, can…

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