Infinite-type cluster algebras have G-fans that are never complete, and rank 3 local behavior falls into six types that correlate with global fan shapes.
Cambrian frameworks for cluster algebras of affine type
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We give a combinatorial model for the exchange graph and g-vector fan associated to any acyclic exchange matrix B of affine type. More specifically, we construct a reflection framework for B in the sense of [N. Reading and D. E. Speyer, "Combinatorial frameworks for cluster algebras"] and establish good properties of this framework. The framework (and in particular the g-vector fan) is constructed by combining a copy of the Cambrian fan for B with an antipodal copy of the Cambrian fan for -B.
fields
math.CO 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Local and global patterns of rank 3 $G$-fans of totally-infinite type
Infinite-type cluster algebras have G-fans that are never complete, and rank 3 local behavior falls into six types that correlate with global fan shapes.