Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abundant configurations in sumsets with one dense summand   We analyze sumsets A+B = {a+b : a in A, b in B} where A,B are sets of
integers, A is infinite, and B has positive upper Banach density. For each k,
we show that A+B contains at least the expected density of k-term arithmetic
progressions based on the density of B, in contrast with an example of
Bergelson, Host, Kra, and Ruzsa. Furthermore, we show that A+B must contain
finite configurations not necessarily found in arbitrary sets of positive
density, in contrast with results of Frantzikinakis, Lesigne, and Wierdl on
sets of k-recurrence.

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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: eess