36 citations · 202 across the 22 of their papers we have counts for
24 papers
Dominance regions for affine cluster algebras
Nathan Reading, Dylan Rupel, Salvatore Stella
We determine dominance regions associated to cluster algebras of affine type. In the most interesting cases, the dominance region is a line segment, which we describe explicitly. M…
Dilogarithm identities of higher degree and cluster -variable periodicity
Zachary Nash, Dylan Rupel
We use the periodicities of cluster groupoid mutations established by Li and the second author to prove that the dilogarithm identities of higher degree obtained by Nakanishi follo…
Dominance Regions for Rank Two Cluster Algebras
Dylan Rupel, Salvatore Stella
We study the polygons defining the dominance order on -vectors in cluster algebras of rank 2.
Symplectic groupoids for cluster manifolds
Songhao Li, Dylan Rupel
We construct symplectic groupoids integrating log-canonical Poisson structures on cluster varieties of type and over both the real and complex numbers.…
Introduction to Cluster Algebras
Max Glick, Dylan Rupel
These are notes for a series of lectures presented at the ASIDE conference 2016. The definition of a cluster algebra is motivated through several examples, namely Markov triples, t…
Cell Decompositions for Rank Two Quiver Grassmannians
Dylan Rupel, Thorsten Weist
We prove that all quiver Grassmannians for exceptional representations of a generalized Kronecker quiver admit a cell decomposition. In the process, we introduce a class of regular…