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…
On Dyck Path Expansion Formulas for Rank 2 Cluster Variables
Amanda Burcroff
In this paper, we simplify and generalize formulas for the expansion of rank 2 cluster variables. In particular, we prove an equivalent, but simpler, description of the colored Dyc…
Pattern-Avoiding Permutation Powers
Amanda Burcroff, Colin Defant
Recently, Bóna and Smith defined strong pattern avoidance, saying that a permutation strongly avoids a pattern if and both avoid . They conjectured that for ev…
Generalized Lyndon Factorizations of Infinite Words
Amanda Burcroff, Eric Winsor
A generalized lexicographic order on words is a lexicographic order where the total order of the alphabet depends on the position of the comparison. A generalized Lyndon word is a…
-Anti-Powers and Other Patterns in Words
Amanda Burcroff
Given a word, we are interested in the structure of its contiguous subwords split into blocks of equal length, especially in the homogeneous and anti-homogeneous cases. We intr…