10 citations · 12 across the 8 of their papers we have counts for
4 papers · 1 filter
Cluster scattering diagrams via quiver moduli and tight gradings
Amanda Burcroff, Kyungyong Lee, Lang Mou +2
We study rank-2 cluster scattering diagrams through moduli spaces of quiver representations and a recently developed combinatorial framework of tight gradings. Combining quiver-the…
Mutations of quivers with 2-cycles
Fang Li, Siyang Liu, Lang Mou +1
We develop a mutation theory for quivers with oriented 2-cycles using a structure called a homotopy, defined as a normal subgroupoid of the quiver's fundamental groupoid. This fram…
Positivity of generalized cluster scattering diagrams
Amanda Burcroff, Kyungyong Lee, Lang Mou
We introduce a new class of combinatorial objects, named tight gradings, which are certain nonnegative integer-valued functions on maximal Dyck paths. Using tight gradings, we deri…
Scattering diagrams, tight gradings, and generalized positivity
Amanda Burcroff, Kyungyong Lee, Lang Mou
In 2013, Lee, Li, and Zelevinsky introduced combinatorial objects called compatible pairs to construct the greedy bases for rank-2 cluster algebras, consisting of indecomposable po…