# Introduction to Cluster Algebras. Chapters 1-3

@article{Fomin2016IntroductionTC, title={Introduction to Cluster Algebras. Chapters 1-3}, author={Sergey Fomin and Lauren K. Williams and Andrei Zelevinsky}, journal={arXiv: Combinatorics}, year={2016} }

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. Mutations of quivers and matrices
Chapter 3. Clusters and seeds

## 48 Citations

### Upper cluster algebras and choice of ground ring

- MathematicsScience China Mathematics
- 2019

We initiate a study of the dependence of the choice of ground ring on the problem on whether a cluster algebra is equal to its upper cluster algebra. A condition for when there is equality of the…

### Combinatorics of X-variables in finite type cluster algebras

- MathematicsJ. Comb. Theory, Ser. A
- 2019

### From frieze patterns to cluster categories

- Mathematics
- 2020

Motivated by Conway and Coxeter's combinatorial results concerning frieze patterns, we sketch an introduction to the theory of cluster algebras and cluster categories for acyclic quivers. The goal is…

### Morsifications and mutations

- MathematicsJournal of the London Mathematical Society
- 2022

We describe and investigate a connection between the topology of isolated singularities of plane curves and the mutation equivalence, in the sense of cluster algebra theory, of the quivers associated…

### LINEAR RELATIONS AND INTEGRABILITY FOR CLUSTER ALGEBRAS FROM AFFINE QUIVERS

- MathematicsGlasgow Mathematical Journal
- 2020

Abstract We consider frieze sequences corresponding to sequences of cluster mutations for affine D- and E-type quivers. We show that the cluster variables satisfy linear recurrences with periodic…

### Cluster algebras and cluster categories associated with triangulated surfaces: an introduction

- Mathematics
- 2020

These are the notes of a three hours minicourse given at the school Winterbraids VIII, CIRM Luminy in March 2018.

### A Note on One-loop Cluster Adjacency in N = 4 SYM

- Mathematics
- 2020

We study cluster adjacency conjectures for amplitudes in maximally supersymmetric Yang-Mills theory. We show that the n-point one-loop NMHV ratio function satisfies Steinmann cluster adjacency. We…

### Combinatorics of $\mathcal{X}$-variables in finite type cluster algebras

- Mathematics
- 2018

We compute the number of $\mathcal{X}$-variables (also called coefficients) of a cluster algebra of finite type when the underlying semifield is the universal semifield. For classical types, these…

### Galois covers ofN = 2 BPS spectra and quantum monodromy

- Physics
- 2015

The BPS spectrum of many 4dN = 2 theories may be seen as the (categorical) Galois cover of the BPS spectrum of a dierent 4d

### Lagrangian fillings for Legendrian links of finite type

- Mathematics
- 2021

We prove that there are at least seeds many exact embedded Lagrangian fillings for Legendrian links of type ADE. We also provide seeds many Lagrangian fillings with certain symmetries for type BCFG.…

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