The Quiver Mutation Database (QMD) is an open research infrastructure for quivers, exchange matrices, and mutation-equivalence classes arising in cluster algebras, representation theory, and related areas of algebra and geometry.
Quiver mutation is a central operation in modern algebraic combinatorics, but its combinatorial complexity grows rapidly. Even for modest numbers of vertices, mutation-equivalence classes can be large, infinite, or difficult to explore systematically. As a result, much of the existing knowledge about mutation classes, invariants, and exceptional phenomena is scattered across papers, personal code, and ad hoc datasets.
QMD is designed to address this gap by providing a curated, citable, and reproducible database of quivers and mutation classes, together with rigorously defined invariants and transparent computational provenance. The project is inspired by successful community resources such as the L-functions and Modular Forms Database (LMFDB) and House of Graphs, and aims to bring similar infrastructure principles to the study of quiver mutation.
FAIR: Findable, Accessible, Interoperable, Reusable
QMD is designed in accordance with the
FAIR Data Principles.
A database that is not findable, accessible to non-experts, integratable with existing
mathematical infrastructure, or reusable is of little use to the mathematical community.
Stable identifiers
Each quiver is assigned a permanent identifier determined by a canonical
representative up to relabeling. Mutation-equivalence classes are
likewise identified by canonical representatives, with clear documentation
of exploration limits when full enumeration is not possible.
Reproducibility and provenance
All computed data are accompanied by metadata describing how the values
were obtained, including algorithmic assumptions, software versions,
and references where applicable.
Forward-facing with room to grow
New invariants, frozen vertices, and skew-symmetrizable matrices are
objects of interest that will be included. The database is built so that
future expansion is a core design principle, not an afterthought.
Accessibility to a mathematical audience
The data should be easily filterable, searchable, viewable, and downloadable.
The goal of the database is to promote data-driven research in the mathematical
community, and that starts with a low-barrier-to-entry public-facing interface.
QMD is intended as a community resource. Suggestions, corrections, and expressions of interest are welcome.
Blake Jackson
University of Connecticut
blake.jackson@uconn.edu