@incollection{goncharov2017ideal, AUTHOR = {Goncharov, A. B.}, TITLE = {Ideal webs, moduli spaces of local systems, and 3d {C}alabi-{Y}au categories}, BOOKTITLE = {Algebra, geometry, and physics in the 21st century: Kontsevich Festschrift}, SERIES = {Progr. Math.}, VOLUME = {324}, PAGES = {31--97}, PUBLISHER = {Birkh\"auser/Springer, Cham}, YEAR = {2017}, DOI = {10.1007/978-3-319-59939-7\_2}, } @article{fock2006moduli, title={Moduli spaces of local systems and higher Teichm{\"u}ller theory}, author={Fock, Vladimir and Goncharov, Alexander}, journal={Publications Math{\'e}matiques de l'IH{\'E}S}, volume={103}, pages={1--211}, year={2006}, DOI = {10.1007/s10240-006-0039-4}, } @article{muller2017twist, AUTHOR = {Muller, Greg and Speyer, David E.}, TITLE = {The twist for positroid varieties}, JOURNAL = {Proc. Lond. Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {115}, YEAR = {2017}, NUMBER = {5}, PAGES = {1014--1071}, DOI = {10.1112/plms.12056}, } @article{schiffler2006cluster, title={A cluster expansion formula ($ A\_n $ case)}, author={Schiffler, Ralf}, journal={arXiv preprint math/0611956}, year={2006} } @misc{postnikov2006total, title={Total positivity, Grassmannians, and networks}, author={Postnikov, Alexander}, eprinttype = {arXiv}, eprint = {math/0609764}, year={2006} } @article{penner1987decorated, AUTHOR = {Penner, R. C.}, TITLE = {The decorated {T}eichm\"uller space of punctured surfaces}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {113}, YEAR = {1987}, NUMBER = {2}, PAGES = {299--339}, URL = {http://projecteuclid.org/euclid.cmp/1104160216}, } @article{cluster4, AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei}, TITLE = {Cluster algebras. {IV}. {C}oefficients}, JOURNAL = {Compos. Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {143}, YEAR = {2007}, NUMBER = {1}, PAGES = {112--164}, DOI = {10.1112/S0010437X06002521}, } @article{cluster1, AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei}, TITLE = {Cluster algebras. {I}. {F}oundations}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {15}, YEAR = {2002}, NUMBER = {2}, PAGES = {497--529}, DOI = {10.1090/S0894-0347-01-00385-X}, } @article{alma9952045080001701, title={The Geometry and Topology of Three-Manifolds}, author={Thurston, WP}, journal={http://www. msri. org/gt3m}, year={1980} } @article{cluster2, AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei}, TITLE = {Cluster algebras. {II}. {F}inite type classification}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {154}, YEAR = {2003}, NUMBER = {1}, PAGES = {63--121}, DOI = {10.1007/s00222-003-0302-y}, URL = {https://doi.org/10.1007/s00222-003-0302-y}, } @article{musiker2011positivity, AUTHOR = {Musiker, Gregg and Schiffler, Ralf and Williams, Lauren}, TITLE = {Positivity for cluster algebras from surfaces}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {227}, YEAR = {2011}, NUMBER = {6}, PAGES = {2241--2308}, DOI = {10.1016/j.aim.2011.04.018}, } @article{banaian2020snake, AUTHOR = {Banaian, Esther and Kelley, Elizabeth}, TITLE = {Snake graphs from triangulated orbifolds}, JOURNAL = {SIGMA Symmetry Integrability Geom. Methods Appl.}, FJOURNAL = {SIGMA. Symmetry, Integrability and Geometry. Methods and Applications}, VOLUME = {16}, YEAR = {2020}, PAGES = {Paper No. 138, 50 pp.}, DOI = {10.3842/SIGMA.2020.138}, URL = {https://doi.org/10.3842/SIGMA.2020.138}, } @article{musiker2022double, AUTHOR = {Musiker, Gregg and Ovenhouse, Nicholas and Zhang, Sylvester W.}, TITLE = {Double dimer covers on snake graphs from super cluster expansions}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {608}, YEAR = {2022}, PAGES = {325--381}, DOI = {10.1016/j.jalgebra.2022.05.033}, } @misc{carroll2003two, title={Two new combinatorial models for the Ptolemy recurrence}, author={Carroll, G. and Price, Gregory}, note={Unpublished memo}, year={2003} } @misc{propp2002lattice, title={Lattice structure for orientations of graphs}, author={Propp, James}, eprinttype = {arXiv}, eprint = {math/0209005}, year={2002} }