Papers by Sergey Fomin

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

Links to my papers: arXiv, Google Scholar, MathSciNet (requires subscription).

Heronian friezes (with L. Setiabrata).

Morsifications and mutations (with P. Pylyavskyy, E. Shustin, and D. Thurston).

Introduction to cluster algebras. Chapters 4-5 (with L. Williams and A. Zelevinsky).

Introduction to cluster algebras. Chapters 1-3 (with L. Williams and A. Zelevinsky).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Papers published before 2000