8 citations · 17 across the 4 of their papers we have counts for
6 papers
On the relationship between green-to-red sequences, local-acyclicity, and upper cluster algebras
Matthew R. Mills
A cluster is a finite set of generators of a cluster algebra. The Laurent Phenomenon of Fomin and Zelevinsky says that any element of a cluster algebra can be written as a Laurent…
Frieze varieties : A characterization of the finite-tame-wild trichotomy for acyclic quivers
Kyungyong Lee, Li Li, Matthew Mills +2
We introduce a new class of algebraic varieties which we call frieze varieties. Each frieze variety is determined by an acyclic quiver. The frieze variety is defined in an elementa…
Properties of minimal mutation-infinite quivers
John W. Lawson, Matthew R. Mills
We study properties of minimal mutation-infinite quivers. In particular we show that every minimal-mutation infinite quiver of at least rank 4 is Louise and has a maximal green seq…
Maximal green sequences for quivers of finite mutation type
Matthew R. Mills
In general, the existence of a maximal green sequence is not mutation invariant. In this paper we show that it is in fact mutation invariant for cluster quivers of finite mutation…
Maximal Green Sequences for Cluster Algebras Associated to the Orientable Surfaces of Genus n with Arbitrary Punctures
Eric Bucher, Matthew R. Mills
It is well known that any triangulation of a marked surface produces a quiver. In this paper we will provide a triangulation for orientable surfaces of genus with an arbitrary…
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
Kyungyong Lee, Li Li, Matthew R. Mills
We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acy…