Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On tropical friezes associated with Dynkin diagrams   Tropical friezes are the tropical analogues of Coxeter-Conway frieze
patterns. In this note, we study them using triangulated categories. A tropical
frieze on a 2-Calabi-Yau triangulated category $\mathcal{C}$ is a function
satisfying a certain addition formula. We show that when $\mathcal{C}$ is the
cluster category of a Dynkin quiver, the tropical friezes on ${\mathcal{C}}$
are in bijection with the $n$-tuples in ${\mathbb{Z}}^n$, any tropical frieze
$f$ on $\mathcal{C}$ is of a special form, and there exists a cluster-tilting
object such that $f$ simultaneously takes non-negative values or non-positive
values on all its indecomposable direct summands. Using similar techniques, we
give a proof of a conjecture of Ringel for cluster-additive functions on stable
translation quivers.

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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg