Sources.bib

@misc{bbh,
  
  doi = {10.48550/ARXIV.MATH/0612213},
  
  url = {https://arxiv.org/abs/math/0612213},
  
  author = {Beineke, Andre and Brüstle, Thomas and Hille, Lutz},
  
  keywords = {Rings and Algebras (math.RA), Representation Theory (math.RT), FOS: Mathematics, FOS: Mathematics, 16G20, 11D25},
  
  title = {Cluster-Cyclic Quivers with three Vertices and the Markov Equation},

}


@misc{MVson,

  doi = {10.48550/ARXIV.1911.00746},
  
  url = {https://arxiv.org/abs/1911.00746},
  
  author = {van Son, Matty},
  
  keywords = {Number Theory (math.NT), FOS: Mathematics, FOS: Mathematics, 11J06 (Primary) 11H55, 11B37, 11B39, 11A55, 11Y65 (Secondary)},
  
  title = {Uniqueness conjectures for extended Markov numbers},
  
  publisher = {arXiv},
  
  year = {2019},
  
  copyright = {arXiv.org perpetual, non-exclusive license}
}


@misc{KLRS,
      title={On the ordering of the Markov numbers}, 
      author={Kyungyong Lee and Li Li and Michelle Rabideau and Ralf Schiffler},
      label = {KLRS},
      eprint={2010.13010},
      archivePrefix={arXiv},
      primaryClass={math.NT}
}


@misc{McSh,
  doi = {10.48550/ARXIV.2101.03316},
  
  url = {https://arxiv.org/abs/2101.03316},
  
  author = {McShane, Greg},
  
  keywords = {Number Theory (math.NT), Differential Geometry (math.DG), Geometric Topology (math.GT), FOS: Mathematics, FOS: Mathematics},
  
  title = {Convexity and Aigner's Conjectures},
  
  publisher = {arXiv},
  
  year = {2021},
  
  copyright = {Creative Commons Attribution 4.0 International}
}


@misc{CS1,
  doi = {10.48550/ARXIV.1711.02461},

  label = {CS1},
  
  url = {https://arxiv.org/abs/1711.02461},
  
  author = {Canakci, Ilke and Schiffler, Ralf},
  
  keywords = {Combinatorics (math.CO), Number Theory (math.NT), FOS: Mathematics, FOS: Mathematics, 11A55 (primary), 05A19, 13F60},
  
  title = {Snake graphs and continued fractions},
  
  publisher = {arXiv},
  
  
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@misc{Sch,
  doi = {10.48550/ARXIV.2302.02185},
  
  url = {https://arxiv.org/abs/2302.02185},
  
  author = {Schiffler, Ralf},
  
  keywords = {Combinatorics (math.CO), Number Theory (math.NT), FOS: Mathematics, FOS: Mathematics, 06A07, 11J06, 05C70, 13F60},
  
  title = {Perfect matching problems in cluster algebras and number theory},
  
  publisher = {arXiv},
  
  year = {2023},
  
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@misc{LS,
      title={Positivity for cluster algebras}, 
      author={Kyungyong Lee and Ralf Schiffler},
      year={2014},
      eprint={1306.2415},
      archivePrefix={arXiv},
      primaryClass={math.CO}
}

@misc{FST,
      title={Cluster algebras and triangulated surfaces. Part I: Cluster complexes}, 
      author={Sergey Fomin and Michael Shapiro and Dylan Thurston},
      year={2007},
      eprint={math/0608367},
      archivePrefix={arXiv},
      primaryClass={math.RA}
}

@misc{CS2,
	doi = {10.1112/s0010437x17007631},
  
	url = {https://doi.org/10.1112%2Fs0010437x17007631},

    label = {CS2},
  
	publisher = {Wiley},
  
	volume = {154},
  
	number = {3},
  
	pages = {565--593},
  
	author = {{\.{I}
}lke {\c{C}}anak{\c{c}}{\i} and Ralf Schiffler}},
  
	title = {Cluster algebras and continued fractions},
  
	journal = {Compositio Mathematica}
}

@article{HW, 
title={G. H. Hardy, and E. M. Wright, An Introduction to the Theory of Numbers (Fourth Edition) (Clarendon Press: Oxford University Press, 1960), 421 pp., 42s.}, 
label = {HW},
volume={12}, 
DOI={10.1017/S0013091500002820}, 
number={3}, 
journal={Proceedings of the Edinburgh Mathematical Society},
publisher={Cambridge University Press}, 
author={Hunter, J.}, 
year={1961}, 
pages={161–161}
}

@misc{CS3, 
      label = {CS3},  
      title={Snake graph calculus and cluster algebras from surfaces}, 
      author={Ilke Canakci and Ralf Schiffler},
      eprint={1209.4617},
      archivePrefix={arXiv},
      primaryClass={math.RT}
}

@book{F, 
label = {F},
place={Berlin}, 
title={Über die Markoffschen zahlen}, publisher={Königliche Akademie der Wissenschaften}, 
author={Frobenius, Georg Ferdinand and Frobenius, Ferdinand Georg and Frobenius, Ferdinand Georg and Frobenius, Ferdinand Georg}, 
} 

@misc{MSW,
      title={Positivity for cluster algebras from surfaces}, 
      author={Gregg Musiker and Ralf Schiffler and Lauren Williams},
      label = {MSW},
      eprint={0906.0748},
      archivePrefix={arXiv},
      primaryClass={math.CO}
}

@misc{FZ1,
      title={Cluster algebras I: Foundations}, 
      author={Sergey Fomin and Andrei Zelevinsky},
      label = {FZ1},
      eprint={math/0104151},
      archivePrefix={arXiv},
      primaryClass={math.RT}
}

@article{Bao,
	doi = {10.1103/physrevd.102.086013},
  
	url = {https://doi.org/10.1103%2Fphysrevd.102.086013},
  
	month = {oct},
  
	publisher = {American Physical Society ({APS})},
  
	volume = {102},
  
	number = {8},
  
	author = {Jiakang Bao and Sebasti{\'{a}
}n Franco and Yang-Hui He and Edward Hirst and Gregg Musiker and Yan Xiao},
  
	title = {Quiver mutations, Seiberg duality, and machine learning},
  
	journal = {Physical Review D}
}
}

@book{A, 
title={Markov’s theorem and 100 years of the uniqueness conjecture}, 
publisher={Springer}, 
label = {A},
author={Aigner, Martin}, 
} 

@misc{MW,
      title={Matrix formulae and skein relations for cluster algebras from surfaces}, 
      author={Gregg Musiker and Lauren Williams},
      label={MW},
      eprint={1108.3382},
      archivePrefix={arXiv},
      primaryClass={math.CO}
}

@misc{GHKK,
      title={Canonical bases for cluster algebras}, 
      author={Mark Gross and Paul Hacking and Sean Keel and Maxim Kontsevich},
      label = {GHKK},
      eprint={1411.1394},
      archivePrefix={arXiv},
      primaryClass={math.AG}
}