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If $\vert A + A \vert = 2\vert A \vert - 1,$ then is $A$ an arithmetic progression?

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#integers #arithmetic-progressions #additive-combinatorics
209
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Expectation of r.v. in the proof of crossing number inequality

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#combinatorics #discrete-mathematics #graph-theory #extremal-combinatorics #additive-combinatorics
66
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Let $A,B$ be nonempty sets of a finite additive group $Z$.Show that there exists an $x\in Z$ such that $1-|A\cap (B+x)|/|Z|\leq(1-|A|/|Z|)(1-|B|/|Z|)$

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#additive-combinatorics #probabilistic-method
75
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Additive Combinatorics: Dyson's transform

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#solution-verification #proof-writing #additive-combinatorics
22
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When is the Frobenius number of a numerical semigroup larger than the maximum of the minimal generating set

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#combinatorics #number-theory #semigroups #monoid #additive-combinatorics
252
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Is there an exponential lower bound for the chromatic number?

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#combinatorics #graph-theory #coloring #additive-combinatorics
61
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About Hahn-Banach Theorem assumption

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#real-analysis #functional-analysis #number-theory #additive-combinatorics #hahn-banach-theorem
34
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Showing that a set of equations have positive density of solutions

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#number-theory #additive-combinatorics #combinatorial-number-theory
32
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Erdos-Szemeredi conjecture orginal paper

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#reference-request #additive-combinatorics
35
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Bound on the number of distinct subset-sums of a given set

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#combinatorics #additive-combinatorics
85
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If $A \subseteq \mathbb{Z}/p\mathbb{Z}$, and $|A| > \frac{p}{3}$, then are there any nontrivial lower bounds for $|AA|$?

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#combinatorics #number-theory #finite-fields #additive-combinatorics
99
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Cauchy Davenport in mod $n$

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#combinatorics #elementary-number-theory #reference-request #contest-math #additive-combinatorics
45
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Arithmetic Triangle Removal Lemma

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#additive-combinatorics #probabilistic-method
93
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Imre Ruzsa Generalisation of Kneser's theorem proof

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#combinatorics #group-theory #reference-request #combinatorial-group-theory #additive-combinatorics
245
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Growth of powers of symmetric subsets in a finite group

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#group-theory #finite-groups #additive-combinatorics

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