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Exercise 1.1.6 in Additive Combinatorics

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#combinatorics #reference-request #additive-combinatorics
107
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Show that $A+B$ contains at least $m+n-1$ elements.

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#combinatorics #additive-combinatorics
69
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Advantage of Fourier transform on $\mathbb{Z}_N$

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#number-theory #additive-combinatorics
182
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Sorting on non-additive ratios

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#number-theory #order-theory #ratio #additive-combinatorics
61
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Asymptotic formula for the integral sequence s(n)

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#combinatorics #group-theory #number-theory #stirling-numbers #additive-combinatorics
168
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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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#sequences-and-series #additive-combinatorics
79
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show that $[n \sqrt{3}]$ is an approximate group

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#group-theory #additive-combinatorics
121
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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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#probability #combinatorics #generating-functions #moment-generating-functions #additive-combinatorics
110
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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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#functional-analysis #normed-spaces #additive-combinatorics
55
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Is that specific function additive under disjoint union?

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#abstract-algebra #group-theory #elementary-set-theory #additive-combinatorics
110
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Does Haar measure have such property?

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#group-theory #measure-theory #additive-combinatorics #borel-sets #haar-measure
50
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number of sums in $\mathbb{Z}_{p^r}$ which are coprime to $p^r$

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#additive-combinatorics #sumset
399
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What do Tao & Vu mean by "additive set"?

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#elementary-number-theory #integers #additive-combinatorics
130
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Is it always true, that $\lim_{n \to \infty} \frac{|A_n \cap H|}{|A_n|} = \frac{1}{[G:H]}$?

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#abstract-algebra #group-theory #limits #finitely-generated #additive-combinatorics
254
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Additive basis of order $2$ (I)

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#sequences-and-series #number-theory #elementary-number-theory #additive-combinatorics

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