Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discordant sets and ergodic Ramsey theory   We explore the properties of non-piecewise syndetic sets with positive upper
density, which we call "discordant", in countably infinite amenable
(semi)groups. Sets of this kind are involved in many questions of Ramsey theory
and manifest the difference in complexity between the classical van der
Waerden's theorem and Szemer\'{e}di's theorem. We generalize and unify old
constructions and obtain new results about these historically interesting sets.
Along the way, we draw from various corners of mathematics, including classical
Ramsey theory, ergodic theory, number theory, and topological and symbolic
dynamics.

18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph