Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Avoiding Monochromatic Solutions to 3-term Equations   Given an equation, the integers $[n] = \{1, 2, \dots, n\}$ as inputs, and the
colors red and blue, how can we color $[n]$ in order to minimize the number of
monochromatic solutions to the equation, and what is the minimum? The answer is
only known for a handful of equations, but much progress has been made on
improving upper and lower bounds on minima for various equations. A
well-studied characteristic an equation, which has its roots in graph Ramsey
theory, is to determine if the minimum number of monochromatic solutions can be
achieved (asymptotically) by uniformly random colorings. Such equations are
called common. We prove that no 3-term equations are common and provide a lower
bound for a specific class of 3-term equations.

34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph