Showing math.COShow all
3 papers · 1 filter
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
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…
math.CO2024
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…