A compendium on the cluster algebra and quiver package in sage

Abstract

This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by gathering data, and by exhibiting and testing conjectures. In this compendium, we include the relevant theory to introduce the reader to cluster algebras assuming no prior background; this exposition has been written to be accessible to an interested undergraduate. Throughout this compendium, we include examples that the user can run in the sage notebook or command line, and then close with a detailed description of the data structures and methods in this package.

62 pages

References in corpus (19)

• Alternating sign matrices and domino tilings
• Cluster algebras and triangulated surfaces. Part II: Lambda lengths
• Quiver varieties and cluster algebras
• Skew-symmetric cluster algebras of finite mutation type
• The combinatorics of frieze patterns and Markoff numbers
• Lattice structure for orientations of graphs
• Dual Teichmuller and lamination spaces
• Q-systems, Heaps, Paths and Cluster Positivity
• KP solitons, total positivity, and cluster algebras
• Categorification of skew-symmetrizable cluster algebras
• Mutation classes of \tilde{A}_n-quivers and derived equivalence classification of cluster tilted algebras of type \tilde{A}_n
• Counting cluster-tilted algebras of type $A_n$
• Symplectic Maps from Cluster Algebras
• Positivity for cluster algebras from surfaces
• Cluster X-varieties at infinity
• Q-system Cluster Algebras, Paths and Total Positivity
• Discrete non-commutative integrability: the proof of a conjecture by M. Kontsevich
• Decomposition Algorithm for Median Graph of Triangulation of a Bordered 2D Surface
• Counting the number of elements in the mutation classes of \tilde{A}_n-quivers

Cited by in corpus (10)

• Introduction to Cluster Algebras. Chapters 1-3
• Cluster integrable systems, q-Painleve equations and their quantization
• Quiver Mutations, Seiberg Duality and Machine Learning
• Quiver mutation and combinatorial DT-invariants
• A survey on maximal green sequences
• Beyond Aztec Castles: Toric Cascades in the $d{P}_3$ Quiver
• Dungeons and Dragons: Combinatorics for the $d{P}_3$ Quiver
• Diagrammatic description of c-vectors and d-vectors of cluster algebras of finite type
• Path description for $q$-characters of fundamental modules in type $C$
• On folded cluster patterns of affine type