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math.CO2025
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…
math.CO2025
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…
math.CO2025
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…