559 citations · 1.2k across the 37 of their papers we have counts for
41 papers
Incidences and tilings
Sergey Fomin, Pavlo Pylyavskyy
We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases…
Long mutation cycles
Sergey Fomin, Scott Neville
A mutation cycle is a cycle in a graph whose vertices are labeled by the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed , w…
Introduction to Cluster Algebras. Chapter 7
Sergey Fomin, Lauren Williams, Andrei Zelevinsky
This is a preliminary draft of Chapter 7 of our forthcoming textbook "Introduction to Cluster Algebras." Chapters 1-3 have been posted as arXiv:1608.05735. Chapters 4-5 have been p…
Coordinate rings and birational charts
Sergey Fomin, George Lusztig
Let be a semisimple simply connected complex algebraic group. Let be the unipotent radical of a Borel subgroup in . We describe the coordinate rings of (resp., …
Expressive curves
Sergey Fomin, Eugenii Shustin
We initiate the study of a class of real plane algebraic curves which we call expressive. These are the curves whose defining polynomial has the smallest number of critical points…
Universal quivers
Sergey Fomin, Kiyoshi Igusa, Kyungyong Lee
We show that for any positive integer , there exists a quiver with vertices and edges such that any quiver on vertices is a full subquiver of a quiver…