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).

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, to appear.

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.

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