559 citations · 1.2k across the 37 of their papers we have counts for
6 papers · 1 filter
Rules of Three for commutation relations
Jonah Blasiak, Sergey Fomin
We investigate the following surprisingly widespread phenomenon which we call The Rule of Three: in order for a particular kind of commutation relation to hold for subsequences of…
Total positivity and cluster algebras
Sergey Fomin
This is a brief and informal introduction to cluster algebras. It roughly follows the historical path of their discovery, made jointly with A.Zelevinsky. Total positivity serves as…
Cluster algebras and triangulated surfaces. Part I: Cluster complexes
Sergey Fomin, Michael Shapiro, Dylan Thurston
We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such…
Cluster algebras IV: Coefficients
Sergey Fomin, Andrei Zelevinsky
We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initia…
Cluster algebras II: Finite type classification
Sergey Fomin, Andrei Zelevinsky
This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those…
Total positivity: tests and parametrizations
Sergey Fomin, Andrei Zelevinsky
An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.