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Results tagged with additive-combinatorics
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user 120369
Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets, Szemerédi's theorem and its ramifications, Gowers uniformity norms, etc. Often combined with the top-level tags nt.number-theory or co.combinatorics. Some additional tags are available for further specialization, including the tags sumsets and sidon-sets.
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Is every positive-density set of positive integers almost rational?
(All the sets in this discussion are sets of positive integers.) I say a set $V$ is “rational” if it satisfies one of the following conditions:
I. $V$ is finite (possibly empty);
II. $V$ can be writ …
- 1,284
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Is there a set of positive integers of density 1 which contains no infinite arithmetic progr...
Let $V$ be a set of positive integers whose natural density is 1. Is it necessarily true that $V$ contains an infinite arithmetic progression?—i.e., that there are non-negative integers $a,b,\nu$ with …
- 1,284