Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequences of Integers with Missing Quotients and Dense Points Without
  Neighbors   Let A be a pre-defined set of rational numbers. We say a set of natural
numbers S is an A-quotient-free set if no ratio of two elements in S belongs to
A. We find the maximal asymptotic density and the maximal upper asymptotic
density of A-quotient-free sets when A belongs to a particular class. It is
known that in the case A = {p, q}, where p, q are coprime integers greater than
one, the latest problem is reduced to evaluation of the largest number of
lattice non-adjacent points in a triangle whose legs lie on coordinate axis. We
prove that this number is achieved by choosing points of the same color in the
checkerboard coloring.

29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg