Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Red sizes of quivers   In this article, we will expand on the notions of maximal green and reddening
sequences for quivers associated to cluster algebras. The existence of these
sequences has been studied for a variety of applications related to Fomin and
Zelevinsky's cluster algebras. Ahmad and Li considered a numerical measure of
how close a quiver is to admitting a maximal green sequence called a red
number. In this paper we generalized this notion to what we call unrestricted
red numbers which are related to reddening sequences. In addition to
establishing this more general framework we completely determine the red
numbers and unrestricted red numbers for all finite mutation type quivers.
Furthermore, we give conjectures on the possible values of red numbers and
unrestricted red numbers in general.

34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs