10 papers
Eventual sign coherence
Amanda Burcroff, Scott Neville
The sign coherence of -vectors is one of the fundamental theorems of cluster algebras with principal coefficients. In 2019, Gekhtman and Nakanishi posed the asymptotic sign cohe…
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…
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…
Higher -Continued Fractions
Amanda Burcroff, Nicholas Ovenhouse, Ralf Schiffler +1
We introduce a -analog of the higher continued fractions introduced by the last three authors in a previous work (together with Gregg Musiker), which are simultaneously a genera…
Broken lines and compatible pairs for rank 2 quantum cluster algebras
Amanda Burcroff, Kyungyong Lee
There have been several combinatorial constructions of universally positive bases in cluster algebras, and these same combinatorial objects play a crucial role in the known proofs…