A cluster algebra approach to presentations of the monoid of uniform block permutations

Semigroups of transformations, relations, partitions, etc. (20M20) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60)

Cites Work

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Lecture notes on cluster algebras
A polynomial realization of the Hopf algebra of uniform block permutations.
Skew-symmetric cluster algebras of finite mutation type
Recognizing cluster algebras of finite type
Derived equivalence classification for cluster-tilted algebras of type \(A_n\).
The Hopf algebra of uniform block permutations.
Quivers with potentials and their representations. I: Mutations.
Cluster algebras. II: Finite type classification
The classification of maximal inverse monoids of matrices
Partial symmetry, reflection monoids and Coxeter groups.
A lattice isomorphism theorem for cluster groups of mutation-Dynkin type \(A_{n}\)
Quiver mutations and Boolean reflection monoids
Braid groups and quiver mutation
Artin group presentations arising from cluster algebras
A geometric model for cluster categories of type \(D_n\).
Cellular algebras and inverse semigroups.
Quiver representations.
Cluster algebras. I: Foundations
Reflection group relations arising from cluster algebras
Coxeter groups, quiver mutations and geometric manifolds
Partial mirror symmetry, lattice presentations and algebraic monoids.
The Mutation Class ofD_nQuivers
Quivers with potentials and their representations II: Applications to cluster algebras
Combinatorial Gelfand models for some semigroups and q-rook monoid algebras
A presentation for the monoid of uniform block permutations
Coxeter Groups and their Quotients Arising from Cluster Algebras
Algebraic Monoids and Renner Monoids
Reflection group presentations arising from cluster algebras
Quivers with relations arising from clusters (𝐴_{𝑛} case)

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