7 citations · 8 across the 2 of their papers we have counts for
14 papers
Cluster algebras: Notes for the CDM-03 conference
Sergey Fomin, Andrei Zelevinsky
This is an expanded version of the notes of our lectures given at the conference "Current Developments in Mathematics 2003" held at Harvard University on November 21--22, 2003. We…
Cluster algebras III: Upper bounds and double Bruhat cells
Arkady Berenstein, Sergey Fomin, Andrei Zelevinsky
We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an…
Polytopal realizations of generalized associahedra
Frederic Chapoton, Sergey Fomin, Andrei Zelevinsky
In hep-th/0111053, a complete simplicial fan was associated to an arbitrary finite root system. It was conjectured that this fan is the normal fan of a simple convex polytope (a ge…
Y-systems and generalized associahedra
Sergey Fomin, Andrei Zelevinsky
We prove, for an arbitrary finite root system, the periodicity conjecture of Al.B.Zamolodchikov concerning Y-systems, a particular class of functional relations arising in the theo…
Cluster algebras I: Foundations
Sergey Fomin, Andrei Zelevinsky
In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
Loop-erased walks and total positivity
Sergey Fomin
We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely,…