Papers by Sergey Fomin

• arXiv
• Google Scholar
• MathSciNet (requires subscription)
• zbMATH

For the papers that have already been published, I would be glad to email the pdf file of the journal version.

• Introduction to Cluster Algebras (with L. Williams and A. Zelevinsky).
  Chapters 1-3: arXiv:1608.05735  
  Chapters 4-5: arXiv:1707.07190  
  Chapter 6: arXiv:2008.09189  
  Chapter 7: arXiv:2106.02160  

• Cyclically ordered quivers (with S. Neville).
   arXiv:2406.03604  

• Incidences and tilings (with P. Pylyavskyy).
   arXiv:2305.07728  

• Long mutation cycles (with S. Neville).
   arXiv:2304.11505  

• Coordinate rings and birational charts (with G. Lusztig).
   Represent. Theory 26 (2022), 1-16.
   arXiv:2102.03608   MR4359428   Zbl 07480521  

• Expressive curves (with E. Shustin).
   Comm. Amer. Math. Soc. 3 (2023), 669-743.
   arXiv:2006.14066   MR4633650  

• Universal quivers (with K. Igusa and K. Lee).
   Algebr. Comb. 4 (2021), 683-702.
   arXiv:2003.01244   MR4311084   Zbl 07406056  

• Heronian friezes (with L. Setiabrata).
   IMRN 2021, 648-694.
   arXiv:1909.01308   MR4198508   Zbl 7379767  

• Morsifications and mutations (with P. Pylyavskyy, E. Shustin, and D. Thurston).
   J. Lond. Math. Soc. 105 (2022), 2478-2554.
   arXiv:1711.10598   MR4440540   Zbl 7730472  

• On semiring complexity of Schur polynomials (with D. Grigoriev, D. Nogneng, and É. Schost).
   Comput. Complexity 27 (2018), 595-616.
   arXiv:1608.05043   MR3868735   Zbl 1408.68072  

• Rules of Three for commutation relations (with J. Blasiak).
   J. Algebra 500 (2018), 193-220.
   arXiv:1608.05042   MR3765453   Zbl 1441.16033  

• Noncommutative Schur functions, switchboards, and Schur positivity (with J. Blasiak).
   Selecta Math. 23 (2017), 727-766.
   arXiv:1510.00657   MR3595905   Zbl 1355.05249  

• Webs on surfaces, rings of invariants, and clusters (with P. Pylyavskyy).
   Proc. Natl. Acad. Sci. USA 111 (2014), no. 27, 9680-9687.
   arXiv:1308.1718   MR3263299   Zbl 1355.53012  

• Subtraction-free complexity, cluster transformations, and spanning trees (with D. Grigoriev and G. Koshevoy).
   Found. Comput. Math. 16 (2016), 1-31.
   arXiv:1307.8425   MR3451422   Zbl 1352.68104  

• Cluster algebras and triangulated surfaces. Part II: Lambda lengths (with D. Thurston).
   Mem. Amer. Math. Soc., 255 (2018), no. 1223.
   arXiv:1210.5569   MR3852257   Zbl 07000309  

• Tensor diagrams and cluster algebras (with P. Pylyavskyy).
   Adv. Math. 300 (2016), 717-787.
   arXiv:1210.1888   MR3534844   Zbl 1386.13062  

• Total positivity and cluster algebras.
   Proceedings of the International Congress of Mathematicians, vol. 2, 2010, 125-145.
   arXiv:1005.1086   MR2827788   Zbl 1226.13015  

• Labeled floor diagrams for plane curves (with G. Mikhalkin).
   J. Eur. Math. Soc. 12 (2010), 1453-1496.
   arXiv:0906.3828   MR2734349   Zbl 1218.14047  

• Cluster algebras and triangulated surfaces. Part I: Cluster complexes (with M. Shapiro and D. Thurston).
   Acta Math. 201 (2008), 83-146.
   arXiv:math/0608367   MR2448067   Zbl 1263.13023  

• Cluster algebras IV: Coefficients (with A. Zelevinsky).
   Compos. Math. 143 (2007), 112-164.
   arXiv:math/0602259   MR2295199   Zbl 1127.16023  

• Generalized cluster complexes and Coxeter combinatorics (with N. Reading).
   Int. Math. Res. Not. 2005:44, 2709-2757.
   arXiv:math/0505085   MR2181310   Zbl 1117.52017  

• Root systems and generalized associahedra (with N. Reading).
   Geometric combinatorics, 63-131, IAS/Park City Math. Ser., 13, Amer. Math. Soc., 2007.
   arXiv:math/0505518   MR2383126   Zbl 1147.52005  

• Cluster algebras: Notes for the CDM-03 conference (with A. Zelevinsky).
   Current Developments in Mathematics, 2003, Int. Press, 2003.
   arXiv:math/0311493   MR2132323   Zbl 1119.05108  

• Cluster algebras III: Upper bounds and double Bruhat cells (with A. Berenstein and A. Zelevinsky).
   Duke Math. J. 126 (2005), 1-52.
   arXiv:math/0305434   MR2110627   Zbl 1135.16013  

• Eigenvalues, singular values, and Littlewood-Richardson coefficients (with W. Fulton, C.-K. Li, and Y.-T. Poon)
   Amer. J. Math. 127 (2005), 101-127.
   arXiv:math/0301307   MR2115662   Zbl 1072.15010  

• Cluster algebras II: Finite type classification (with A. Zelevinsky)
   Invent. Math. 154 (2003), 63-121.
   arXiv:math/0208229   MR2004457   Zbl 1054.17024  

• Polytopal realizations of generalized associahedra (with F. Chapoton and A. Zelevinsky)
   Canad. Math. Bull. 45 (2002), 537-566.
   arXiv:math/0202004   MR1941227   Zbl 1018.52007  

• Y-systems and generalized associahedra (with A. Zelevinsky)
   Ann. of Math. 158 (2003), 977-1018.
   arXiv:hep-th/0111053   MR2031858   Zbl 1057.52003  

• The Laurent phenomenon (with A. Zelevinsky)
   Adv. in Appl. Math. 28 (2002), 119-144.
   arXiv:math/0104241   MR1888840   Zbl 1012.05012  

• Cluster algebras I: Foundations (with A. Zelevinsky)
   J. Amer. Math. Soc. 15 (2002), 497-529.
   arXiv:math/0104151   MR1887642   Zbl 1021.16017  

• Loop-erased walks and total positivity
   Trans. Amer. Math. Soc. 353 (2001), 3563-3583.
   arXiv:math/0004083   MR1837248   Zbl 0973.15014  

• Finite posets and Ferrers shapes (with T. Britz)
   Adv. Math. 158 (2001), 86-127.
   arXiv:math/9912126   MR1814900   Zbl 0986.06003  

• Stratified spaces formed by totally positive varieties (with M. Shapiro)
   Michigan Math. J. 48 (2000), 253-270.
   arXiv:math/9912125   MR1786489   Zbl 0986.06003  

• Total positivity: tests and parametrizations (with A. Zelevinsky)
   Math. Intelligencer 22 (2000), 23-33.
   arXiv:math/9912128   MR1745560   Zbl 1052.15500  

• Totally nonnegative and oscillatory elements in semisimple groups (with A. Zelevinsky)
   Proc. Amer. Math. Soc. 128 (2000), 3749-3759.
   arXiv:math/9811100   MR1694341   Zbl 0953.22016  

• Recognizing Schubert cells (with A. Zelevinsky)
   J. Algebraic Combin. 12 (2000), 37-57.
   arXiv:math/9807079   MR1791445   Zbl 1056.14504  

• Fibered quadratic Hopf algebras related to Schubert calculus (with C. Procesi)
   J. Algebra 230 (2000), 174-183.
   preprint   MR1774762   Zbl 0962.16028  

Papers published before 2000