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Results tagged with additive-combinatorics
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user 119533
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.
5
votes
2
answers
350
views
Nontrivial expansion in sumsets
Let $A \subset \mathbb{Z}/p$, let $f$ be a function on $\mathbb{Z}/p$ and let $B:=\{f(a): a \in A\}$.
Can we conclude that $|A+B|$ is large if $f$ is a sufficiently "nice" function? For instance say …
- 383
5
votes
0
answers
839
views
Increasing sequences in polynomial progressions modulo p
In a random permutation on $n$ elements one expects the largest increasing and decreasing sequences to have size $(2+o(1))\sqrt{n}$. Is it known if this same property holds in sequences given by poly …
- 383
8
votes
Accepted
Is there any relationship between Szemerédi's theorem and Sunflower conjecture?
I do not know of a direct connection to Roth or Szemerédi over the integers. However, the paper
N. Alon, A. Shpilka and C. Umans, On Sunflowers and Matrix Multiplication, 2012 IEEE 27th Conference o …
- 383
2
votes
Accepted
Instance of polynomial van der Waerden without good bounds
Isn't this paper the most up to date? I believe the introduction covers all of the relevant literature.
"Proving a fully general quantitative polynomial Szemerédi theorem remains a very challenging o …
- 383
5
votes
1
answer
353
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Primitive recursive bounds for multidimensional polynomial vdW / HJ
In Shelah's paper 679, he proves primitive recursive bounds for the polynomial Hales-Jewett theorem and thus for the polynomial van der Waerden theorem.
How about for the multidimensional polynomial H …
- 383