Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial frameworks for cluster algebras   We develop a general approach to finding combinatorial models for cluster
algebras. The approach is to construct a labeled graph called a framework. When
a framework is constructed with certain properties, the result is a model
incorporating information about exchange matrices, principal coefficients,
g-vectors, and g-vector fans. The idea behind frameworks arises from Cambrian
combinatorics and sortable elements, and in this paper, we use sortable
elements to construct a framework for any cluster algebra with an acyclic
initial exchange matrix. This Cambrian framework yields a model of the entire
exchange graph when the cluster algebra is of finite type. Outside of finite
type, the Cambrian framework models only part of the exchange graph. In a
forthcoming paper, we extend the Cambrian construction to produce a complete
framework for a cluster algebra whose associated Cartan matrix is of affine
type.

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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
16
The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th