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@article{moz1,
  title={An Expansion Formula for Decorated Super-{Teichm\"uller} Spaces},
  author={Musiker, Gregg and Ovenhouse, Nicholas and Zhang, Sylvester W},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  volume={17},
  year={2021},
  publisher={},

}
@misc{mosz,
  title={Higher Dimer Covers on Snake Graphs},
  author={Musiker, Gregg and Ovenhouse, Nicholas and Schiffler, Ralf and Zhang, Sylvester W},
  note={In preparation},
  year = {2023},

}
@article{moz2,
	title = {Double dimer covers on snake graphs from super cluster expansions},
	volume = {608},
	copyright = {All rights reserved},
	issn = {0021-8693},
	journal = {Journal of Algebra},
	author = {Musiker, Gregg and Ovenhouse, Nicholas and Zhang, Sylvester W.},
	year = {2022},
	keywords = {Cluster algebras, Decorated super-{T}eichm\"uller spaces, Double dimers, Snake graphs},
	pages = {325--381},
}


@misc{moz3,
  title={Matrix Formulae for Decorated Super {T}eichm\"uller Spaces},
  author={Musiker, Gregg and Ovenhouse, Nicholas and Zhang, Sylvester W},
  eprint={2208.13664},
  year={2022}
}


@article{cr_07,
	title        = {Dimers on surface graphs and spin structures. {I}},
	author       = {Cimasoni, David and Reshetikhin, Nicolai},
	year         = 2007,
	journal      = {Communications in Mathematical Physics},
	publisher    = {Springer},
	volume       = 275,
	number       = 1,
	pages        = {187--208}
}
@article{cr_08,
	title        = {Dimers on surface graphs and spin structures. {II}},
	author       = {Cimasoni, David and Reshetikhin, Nicolai},
	year         = 2008,
	journal      = {Communications in Mathematical Physics},
	publisher    = {Springer},
	volume       = 281,
	number       = 2,
	pages        = 445
}
@article{fz_02,
	title        = {Cluster algebras {I}: foundations},
	author       = {Fomin, Sergey and Zelevinsky, Andrei},
	year         = 2002,
	journal      = {Journal of the American Mathematical Society},
	volume       = 15,
	number       = 2,
	pages        = {497--529}
}

@article{fz_02b,
  title={Cluster algebras II: Finite type classification},
  author={Fomin, Sergey and Zelevinsky, Andrei},
  journal={arXiv preprint math/0208229},
  year={2002}
}

@article{fst_08,
	title        = {Cluster algebras and triangulated surfaces. Part {I}: Cluster complexes},
	author       = {Fomin, Sergey and Shapiro, Michael and Thurston, Dylan},
	year         = 2008,
	journal      = {Acta Mathematica},
	publisher    = {Springer},
	volume       = 201,
	number       = 1,
	pages        = {83--146}
}
@article{gsv_05,
	title        = {Cluster algebras and {W}eil-{P}etersson forms},
	author       = {Gekhtman, Michael and Shapiro, Michael and Vainshtein, Alek},
	year         = 2005,
	journal      = {Duke Mathematical Journal},
	publisher    = {Duke University Press},
	volume       = 127,
	number       = 2,
	pages        = {291--311}
}
@article{fg_06,
	title        = {Moduli spaces of local systems and higher {T}eichm{\"u}ller theory},
	author       = {Fock, Vladimir and Goncharov, Alexander},
	year         = 2006,
	journal      = {Publications Math{\'e}matiques de l'IH{\'E}S},
	volume       = 103,
	pages        = {1--211}
}
@article{schiffler_08,
	title        = {A cluster expansion formula (${A}_n$ case)},
	author       = {Schiffler, Ralf},
	year         = 2008,
	journal      = {The Electronic Journal of Combinatorics},
	volume       = 15,
	number       = {R64},
	pages        = 1
}
@article{ms10,
	title        = {Cluster expansion formulas and perfect matchings},
	author       = {Musiker, Gregg and Schiffler, Ralf},
	year         = 2010,
	journal      = {Journal of Algebraic Combinatorics},
	publisher    = {Springer},
	volume       = 32,
	number       = 2,
	pages        = {187--209}
}
@article{msw_11,
	title        = {Positivity for cluster algebras from surfaces},
	author       = {Musiker, Gregg and Schiffler, Ralf and Williams, Lauren},
	year         = 2011,
	journal      = {Advances in Mathematics},
	publisher    = {Elsevier},
	volume       = 227,
	number       = 6,
	pages        = {2241--2308}
}
@article{yurikusa_19,
	title        = {Cluster expansion formulas in type {A}},
	author       = {Yurikusa, Toshiya},
	year         = 2019,
	journal      = {Algebras and Representation Theory},
	publisher    = {Springer},
	volume       = 22,
	number       = 1,
	pages        = {1--19}
}
@book{penner_12,
	title        = {Decorated {T}eichm{\"u}ller theory},
	author       = {Penner, Robert C},
	year         = 2012,
	publisher    = {European Mathematical Society},
	volume       = 1
}
@article{pz_19,
	title        = {Decorated super-{T}eichm{\"u}ller space},
	author       = {Penner, RC and Zeitlin, Anton M},
	year         = 2019,
	journal      = {Journal of Differential Geometry},
	publisher    = {Lehigh University},
	volume       = 111,
	number       = 3,
	pages        = {527--566}
}
@article{cr_88,
	title        = {Super {R}iemann surfaces: uniformization and {T}eichm{\"u}ller theory},
	author       = {Crane, Louis and Rabin, Jeffrey M},
	year         = 1988,
	journal      = {Communications in Mathematical Physics},
	publisher    = {Springer},
	volume       = 113,
	number       = 4,
	pages        = {601--623}
}
@article{berenstein2005quantum,
	title        = {Quantum cluster algebras},
	author       = {Berenstein, Arkady and Zelevinsky, Andrei},
	year         = 2005,
	journal      = {Advances in Mathematics},
	publisher    = {Elsevier},
	volume       = 195,
	number       = 2,
	pages        = {405--455}
}
@article{berenstein2018noncommutative,
	title        = {Noncommutative marked surfaces},
	author       = {Berenstein, Arkady and Retakh, Vladimir},
	year         = 2018,
	journal      = {Advances in Mathematics},
	publisher    = {Elsevier},
	volume       = 328,
	pages        = {1010--1087}
}

@article{os_18,
	title        = {Cluster algebras with {G}rassmann variables},
	author       = {Ovsienko, Valentin and Shapiro, Michael},
	year         = 2019,
	journal      = {Electron. Res. Announc. Math. Sci.},
	volume       = 26,
	pages        = {1--15},
	doi          = {10.3934/era.2019.26.001},
	url          = {https://doi-org.ezp1.lib.umn.edu/10.3934/era.2019.26.001},
	fjournal     = {Electronic Research Announcements in Mathematical Sciences},
	mrclass      = {13F60},
	mrnumber     = 3959333
}
@article{lmrs_21,
	title        = {An Introduction to Supersymmetric Cluster Algebras},
	author       = {Li, Li and Mixco, James and Ransingh, B and Srivastava, Ashish K},
	year         = 2021,
	journal      = {The Electronic Journal of Combinatorics},
	pages        = {P1--30}
}


@article{sv09,
  title={On super {P}l{\"u}cker embedding and cluster algebras},
  author={Shemyakova, Ekaterina and Voronov, Theodore},
  journal={Selecta Mathematica},
  volume={28},
  number={2},
  pages={1--58},
  year={2022},
  publisher={Springer}
}


@article{OT18,
	title        = {Dual numbers, weighted quivers, and extended {S}omos and {G}ale-{R}obinson sequences},
	author       = {Ovsienko, Valentin and Tabachnikov, Serge},
	year         = 2018,
	journal      = {Algebr. Represent. Theory},
	volume       = 21,
	number       = 5,
	pages        = {1119--1132},
	doi          = {10.1007/s10468-018-9779-3},
	issn         = {1386-923X},
	url          = {https://doi-org.ezp1.lib.umn.edu/10.1007/s10468-018-9779-3},
	fjournal     = {Algebras and Representation Theory},
	mrclass      = {11B37 (13F60 16G20)},
	mrnumber     = 3855676,
	mrreviewer   = {Min Huang}
}
@article{o_15,
	title        = {A step towards cluster superalgebras},
	author       = {Valetin Ovsienko},
	year         = 2015,
	journal      = {arXiv preprint arXiv:1503.01894}
}
@article{M-GOT15,
	title        = {Introducing supersymmetric frieze patterns and linear difference operators},
	author       = {Morier-Genoud, Sophie and Ovsienko, Valentin and Tabachnikov, Serge},
	year         = 2015,
	journal      = {Math. Z.},
	volume       = 281,
	number       = {3-4},
	pages        = {1061--1087},
	doi          = {10.1007/s00209-015-1520-x},
	issn         = {0025-5874},
	url          = {https://doi-org.ezp1.lib.umn.edu/10.1007/s00209-015-1520-x},
	note         = {With an appendix by Alexey Ustinov},
	fjournal     = {Mathematische Zeitschrift},
	mrclass      = {14M30 (13F60 81Q60)},
	mrnumber     = 3421653,
	mrreviewer   = {Ralf Schiffler}
}
@article{ip2018n,
	title        = {$\mathcal{N}=2$ super-{T}eichm{\"u}ller theory},
	author       = {Ip, Ivan CH and Penner, Robert C and Zeitlin, Anton M},
	year         = 2018,
	journal      = {Advances in Mathematics},
	publisher    = {Elsevier},
	volume       = 336,
	pages        = {409--454}
}
@article{mcshane,
	title        = {Super {M}c{S}hane identity},
	author       = {Huang, Y. and Penner, R.C. and  Zeitlin, A.M.},
	year         = 2019,
	journal      = {arXiv preprint arXiv:1907.09978}
}

@article{propp05,
	title        = {The combinatorics of frieze patterns and {M}arkoff numbers},
	author       = {Propp, James},
	year         = 2005,
	journal      = {arXiv preprint math/0511633}
}
@article{propp02,
	title        = {Lattice structure for orientations of graphs},
	author       = {Propp, James},
	year         = 2002,
	journal      = {arXiv preprint math/0209005}
}
@article{claussen20,
	title        = {Expansion posets for polygon cluster algebras},
	author       = {Claussen, Andrew},
	year         = 2020,
	journal      = {arXiv preprint arXiv:2005.02083}
}
@article{msw13,
	title        = {Bases for cluster algebras from surfaces},
	author       = {Musiker, Gregg and Schiffler, Ralf and Williams, Lauren},
	year         = 2013,
	journal      = {Compositio Mathematica},
	publisher    = {London Mathematical Society},
	volume       = 149,
	number       = 2,
	pages        = {217--263}
}
@article{mw13,
  title={Matrix formulae and skein relations for cluster algebras from surfaces},
  author={Musiker, Gregg and Williams, Lauren},
  journal={International Mathematics Research Notices},
  volume={2013},
  number={13},
  pages={2891--2944},
  year={2013},
  publisher={OUP}
}
@article{mss21,
	title        = {On a rank-unimodality conjecture of {M}orier-{G}enoud and {O}vsienko},
	author       = {McConville, Thomas and Sagan, Bruce E and Smyth, Clifford},
	year         = 2021,
	journal      = {Discrete Mathematics},
	publisher    = {Elsevier},
	volume       = 344,
	number       = 8,
	pages        = 112483
}
@article{st_09,
	title        = {On cluster algebras arising from unpunctured surfaces},
	author       = {Schiffler, Ralf and Thomas, Hugh},
	year         = 2009,
	journal      = {International Mathematics Research Notices},
	publisher    = {OUP},
	volume       = 2009,
	number       = 17,
	pages        = {3160--3189}
}
@article{llm_15,
	title        = {A combinatorial formula for certain elements of upper cluster algebras},
	author       = {Lee, Kyungyong and Li, Li and Mills, Matthew R},
	year         = 2015,
	journal      = {SIGMA. Symmetry, Integrability and Geometry: Methods and Applications},
	publisher    = {SIGMA. Symmetry, Integrability and Geometry: Methods and Applications},
	volume       = 11,
	pages        = {049}
}
@article{MusPropp,
	title        = {Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type},
	author       = {Musiker, Gregg and Propp, James},
	year         = 2007,
	journal      = {The Electronic Journal of Combinatorics},
	volume       = 14,
	number       = {R15},
	pages        = 1
}
@inproceedings{mgo_20,
	title        = {$q$-Deformed Rationals and $q$-Continued Fractions},
	author       = {Morier-Genoud, Sophie and Ovsienko, Valentin},
	year         = 2020,
	booktitle    = {Forum of Mathematics, Sigma},
	volume       = 8,
	organization = {Cambridge University Press}
}
@article{hoggatt1969compositions,
	title        = {Compositions and {F}ibonacci numbers},
	author       = {Hoggatt Jr, VE and Lind, DA},
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@article{lucas1878theorie,
	title        = {Th{\'e}orie des fonctions num{\'e}riques simplement p{\'e}riodiques},
	author       = {Lucas, Edouard},
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	journal      = {American Journal of Mathematics},
	publisher    = {JSTOR},
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@article{czabarka2015discrete,
	title        = {A Discrete Convolution on the Generalized {H}osoya Triangle.},
	author       = {Czabarka, {\'E}va and Fl{\'o}rez, Rigoberto and Junes, Leandro},
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@article{gunawan2019cluster,
	title        = {Cluster algebraic interpretation of infinite friezes},
	author       = {Gunawan, Emily and Musiker, Gregg and Vogel, Hannah},
	year         = 2019,
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	publisher    = {Elsevier},
	volume       = 81,
	pages        = {22--57}
}

@phdthesis{bouschbacher_13,
  title={Shear coordinates on the super Teichm{\"u}ller space},
  author={Bouschbacher, Fabien},
  year={2013},
  school={Universit{\'e} de Strasbourg}
}

@article{ovsienko_22,
  title={Shadow Sequences of Integers: From Fibonacci to Markov and Back},
  author={Ovsienko, Valentin},
  journal={The Mathematical Intelligencer},
  pages={1--5},
  year={2022},
  publisher={Springer}
}

@article{myers1971,
  title={Number of spanning trees in a wheel},
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@article{rabideau2020continued,
  title={Continued fractions and orderings on the {M}arkov numbers},
  author={Rabideau, Michelle and Schiffler, Ralf},
  journal={Advances in Mathematics},
  volume={370},
  pages={107231},
  year={2020},
  publisher={Elsevier}
}

@article{shemyakova2022super,
  title={On super cluster algebras based on super {P}l{\"u}cker and super Ptolemy relations},
  author={Shemyakova, Ekaterina},
  journal={arXiv preprint arXiv:2206.12072},
  year={2022}
}



@misc{conley2022shadows,
  title={Shadows of rationals and irrationals: supersymmetric continued fractions and the super modular group},
  author={Conley, Charles H and Ovsienko, Valentin},
  eprint={2209.10426},
  year={2022}
}