559 citations · 1k across the 44 of their papers we have counts for
44 papers
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…
Introduction to Cluster Algebras. Chapters 1-3
Sergey Fomin, Lauren Williams, Andrei Zelevinsky
This is a preliminary draft of Chapters 1-3 of our forthcoming textbook "Introduction to Cluster Algebras." This installment contains: Chapter 1. Total positivity Chapter 2. Mutati…
The existence of greedy bases in rank 2 quantum cluster algebras
Kyungyong Lee, Li Li, Dylan Rupel +1
We establish the existence of a quantum lift of the greedy basis.
Strongly primitive species with potentials I: Mutations
Daniel Labardini-Fragoso, Andrei Zelevinsky
Motivated by the mutation theory of quivers with potentials developed by Derksen-Weyman-Zelevinsky, and the representation-theoretic approach to cluster algebras it provides, we pr…
Positivity and tameness in rank 2 cluster algebras
Kyungyong Lee, Li Li, Andrei Zelevinsky
We study the relationship between the positivity property in a rank 2 cluster algebra, and the property of such an algebra to be tame. More precisely, we show that a rank 2 cluster…
Greedy elements in rank 2 cluster algebras
Kyungyong Lee, Li Li, Andrei Zelevinsky
A lot of recent activity in the theory of cluster algebras has been directed towards various constructions of "natural" bases in them. One of the approaches to this problem was dev…