@article{snakegraphcalculus1, title={Snake graph calculus and cluster algebras from surfaces}, author={Canakci, Ilke and Schiffler, Ralf}, journal={Journal of Algebra}, volume={382}, pages={240--281}, year={2013}, publisher={Elsevier} } @article{FST-I, Author = {Fomin, Sergey and Shapiro, Michael and Thurston, Dylan}, Journal = {Acta Mathematica}, Title = {Cluster algebras and triangulated surfaces. Part I: Cluster complexes}, volume = {201}, Year = {2008}} @article{FZ2002, ISSN = {08940347, 10886834}, author = {Sergey Fomin and Andrei Zelevinsky}, journal = {Journal of the American Mathematical Society}, number = {2}, pages = {497--529}, publisher = {American Mathematical Society}, title = {Cluster Algebras I: Foundations}, volume = {15}, year = {2002} } @book{fomin2018cluster, title={Cluster algebras and triangulated surfaces Part II: Lambda lengths}, author={Fomin, Sergey and Thurston, Dylan}, volume={255}, number={1223}, year={2018}, publisher={American Mathematical Society} } @article{geiss2022schemes, title={Schemes of modules over gentle algebras and laminations of surfaces}, author={Gei{\ss}, Christof and Labardini-Fragoso, Daniel and Schr{\"o}er, Jan}, journal={Selecta Mathematica}, volume={28}, number={1}, pages={8}, year={2022}, publisher={Springer} } @article{musiker2013bases, title={Bases for cluster algebras from surfaces}, author={Musiker, Gregg and Schiffler, Ralf and Williams, Lauren}, journal={Compositio Mathematica}, volume={149}, number={2}, pages={217--263}, year={2013}, publisher={London Mathematical Society} } @article{musiker2013, author = {Musiker, Gregg and Williams, Lauren}, journal = {International Mathematics Research Notices. IMRN}, title = {Matrix formulae and skein relations for cluster algebras from surfaces}, volume={2013}, year={2013}, pages={2891-2944}, publisher={Oxford University Press} } @article{musiker2011positivity, title={Positivity for cluster algebras from surfaces}, author={Musiker, Gregg and Schiffler, Ralf and Williams, Lauren}, journal={Advances in Mathematics}, volume={227}, number={6}, pages={2241--2308}, year={2011}, publisher={Elsevier} } @misc{oğuz2024cluster, title={Cluster Expansions: T-walks, Labeled Posets and Matrix Calculations}, author={Ezgi Kantarcı Oğuz and Emine Yıldırım}, year={2024}, eprint={2211.08011}, archivePrefix={arXiv}, primaryClass={math.CO} } @book{palu2021non, title={Non-Kissing Complexes and Tau-Tilting for Gentle Algebras}, author={Palu, Yann and Pilaud, Vincent and Plamondon, Pierre-Guy}, volume={274}, year={2021}, publisher={American Mathematical Society} } @misc{wilson2020surface, title={Surface cluster algebra expansion formulae via loop graphs}, EPRINTTYPE = {arxiv}, author={Wilson, Jon}, EPRINT ={2006.13218}, year={2020} } @book{FT-II, title={Cluster algebras and triangulated surfaces Part II: Lambda lengths}, author={Fomin, Sergey and Thurston, Dylan}, volume={255}, number={1223}, year={2018}, journal={American Mathematical Society} } @article{ccanakcci2020snake, title={Snake graphs and continued fractions}, author={Canakci, Ilke and Schiffler, Ralf}, journal={European Journal of Combinatorics}, volume={86}, pages={103081}, year={2020}, publisher={Elsevier} } @misc{pilaud2023posets, title={Posets for $F$-polynomials in cluster algebras from surfaces}, EPRINTTYPE = {arxiv}, author={Pilaud, Vincent and Reading, Nathan and Schroll, Sibylle}, EPRINT ={2311.06033}, year={2023} } @misc{Mandel2023, title={Bracelets bases are theta bases}, EPRINTTYPE = {arxiv}, author={Travis Mandel and Fan Qin}, EPRINT ={2301.11101}, year={2023} } @misc{Weng2023, title={$F$-Polynomials of Donaldson-Thomas Transformations}, EPRINTTYPE = {arxiv}, author={Daping Weng}, EPRINT ={2303.03466}, year={2023} }