Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: John-type theorems for generalized arithmetic progressions and iterated
  sumsets   A classical theorem of Fritz John allows one to describe a convex body, up to
constants, as an ellipsoid. In this article we establish similar descriptions
for generalized (i.e. multidimensional) arithmetic progressions in terms of
proper (i.e. collision-free) generalized arithmetic progressions, in both
torsion-free and torsion settings. We also obtain a similar characterization of
iterated sumsets in arbitrary abelian groups in terms of progressions, thus
strengthening and extending recent results of Szemer\'edi and Vu.

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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin