Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partition regularity in the rationals   A system of homogeneous linear equations with integer coefficients is
partition regular if, whenever the natural numbers are finitely coloured, the
system has a monochromatic solution. The Finite Sums theorem provided the first
example of an infinite partition regular system of equations. Since then, other
such systems of equations have been found, but each can be viewed as a
modification of the Finite Sums theorem.
  We present here a new infinite partition regular system of equations that
appears to arise in a genuinely different way. This is the first example of a
partition regular system in which a variable occurs with unbounded
coefficients. A modification of the system provides an example of a system that
is partition regular over Q but not N, settling another open problem.

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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat