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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…
math.CO2024
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…
math.QA2024
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…