Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unistructurality of cluster algebras of type ${\widetilde{\mathbb{A}}}$   It is conjectured by Ibrahim Assem, Ralf Schiffler and Vasilisa Shramchenko
in "Cluster Automorphisms and Compatibility of Cluster Variables" that every
cluster algebra is unistructural, that is to say, that the set of cluster
variables determines uniquely the cluster algebra structure. In other words,
there exists a unique decomposition of the set of cluster variables into
clusters. This conjecture has been proven to hold true for algebras of type
Dynkin or rank 2 by Assem, Schiffler and Shramchenko. The aim of this paper is
to prove it for algebras of type ${\widetilde{\mathbb{A}}}$. We use
triangulations of annuli and algebraic independence of clusters to prove
unistructurality for algebras arising from annuli, which are of type
${\widetilde{\mathbb{A}}}$. We also prove the automorphism conjecture from
Assem, Schiffler and Shramchenko for algebras of type
${\widetilde{\mathbb{A}}}$ as a direct consequence.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs