Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational Polygons: Odd Compression Ratio and Odd Plane Coverings   Let P be a polygon with rational vertices in the plane. We show that for any
finite odd-sized collection of translates of P, the area of the set of points
lying in an odd number of these translates is bounded away from 0 by a constant
depending on P alone. The key ingredient of the proof is a construction of an
odd cover of the plane by translates of P. That is, we establish a family F of
translates of P covering (almost) every point in the plane a uniformly bounded
odd number of times.

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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex