List questions from additive-combinatorics

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101

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Show that $A+B$ contains at least $m+n-1$ elements.

Published on 23 Mar 2026 - 9:38

62

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Advantage of Fourier transform on $\mathbb{Z}_N$

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174

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Sorting on non-additive ratios

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53

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Asymptotic formula for the integral sequence s(n)

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159

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Show that $|A+A| < 2.5 |A| $ with $A = \{ [n \sqrt{2}] : 1 \leq n \leq N \}$

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74

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show that $[n \sqrt{3}]$ is an approximate group

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113

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A combinatoric solution (closed expression) for $\sum_{k=i}^n \binom{n}{k}p^k(1-p)^{n-k}$

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103

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On Gowers' approach of Green-Tao Theorem ($\mathcal{D}f$s span $L^q(\mathbb{Z}_N)$).

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50

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Is that specific function additive under disjoint union?

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103

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Does Haar measure have such property?

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42

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number of sums in $\mathbb{Z}_{p^r}$ which are coprime to $p^r$

Published on 19 Mar 2026 - 17:08

394

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What do Tao & Vu mean by "additive set"?

Published on 23 Mar 2026 - 22:15

123

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Is it always true, that $\lim_{n \to \infty} \frac{|A_n \cap H|}{|A_n|} = \frac{1}{[G:H]}$?

Published on 24 Mar 2026 - 14:54

248

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Additive basis of order $2$ (I)

Published on 24 Mar 2026 - 7:37

List Question

Exercise 1.1.6 in Additive Combinatorics

Show that $A+B$ contains at least $m+n-1$ elements.

Advantage of Fourier transform on $\mathbb{Z}_N$

Sorting on non-additive ratios

Asymptotic formula for the integral sequence s(n)

Show that $|A+A| < 2.5 |A| $ with $A = \{ [n \sqrt{2}] : 1 \leq n \leq N \}$

show that $[n \sqrt{3}]$ is an approximate group

A combinatoric solution (closed expression) for $\sum_{k=i}^n \binom{n}{k}p^k(1-p)^{n-k}$

On Gowers' approach of Green-Tao Theorem ($\mathcal{D}f$s span $L^q(\mathbb{Z}_N)$).

Is that specific function additive under disjoint union?

Does Haar measure have such property?

number of sums in $\mathbb{Z}_{p^r}$ which are coprime to $p^r$

What do Tao & Vu mean by "additive set"?

Is it always true, that $\lim_{n \to \infty} \frac{|A_n \cap H|}{|A_n|} = \frac{1}{[G:H]}$?

Additive basis of order $2$ (I)

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