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Documents  11B75 | enregistrements trouvés : 4

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Erdös and Sárközy asked the maximum size of a subset of the first $N$ integers with no two elements adding up to a perfect square. In this talk we prove that the tight answer is $\frac{11}{32}N$ for sufficiently large $N$. We are going to prove some stability results also. This is joint work with Simao Herdade and Ayman Khalfallah.

05A18 ; 11B75

Given a subset A of an additive group, how small can the sumset $A+A = \lbrace a+a' : a, a' \epsilon$ $A \rbrace$ be ? And what can be said about the structure of $A$ when $A + A$ is very close to the smallest possible size ? The aim of this talk is to partially answer these two questions when A is either a subset of $\mathbb{Z}$, $\mathbb{Z}/n\mathbb{Z}$, $\mathbb{R}$ or $\mathbb{T}$ and to explain how in this problem discrete and continuous setting are linked. This should also illustrate two important principles in additive combinatorics : reduction and rectification.
This talk is partially based on some joint work with Pablo Candela and some other work with Paul Péringuey.
Given a subset A of an additive group, how small can the sumset $A+A = \lbrace a+a' : a, a' \epsilon$ $A \rbrace$ be ? And what can be said about the structure of $A$ when $A + A$ is very close to the smallest possible size ? The aim of this talk is to partially answer these two questions when A is either a subset of $\mathbb{Z}$, $\mathbb{Z}/n\mathbb{Z}$, $\mathbb{R}$ or $\mathbb{T}$ and to explain how in this problem discrete and continuous ...

11B13 ; 11B83 ; 11B75

Multi angle  Incidences in Cartesian products
Solymosi, Jozsef (Auteur de la Conférence) | CIRM (Editeur )

Various problems in additive combinatorics can be translated to a question about incidences in Cartesian products. A well known example is Elekes' treatment of the sum-product problem but there are many more applications of incidence bounds to arithmetic problems. I will review the classical applications and show some recent results.

11B75 ; 11B13 ; 52C10 ; 05Dxx

We improve a result of Solymosi on sum-products in $\mathbb{R}$, namely, we prove that max $(|A+A|,|AA|\gg |A|^{4/3+c}$, where $c>0$ is an absolute constant. New lower bounds for sums of sets with small product set are found. Previous results are improved effectively for sets $A\subset \mathbb{R}$ with $|AA| \le |A|^{4/3}$. Joint work with I. D. Schkredov.

11B13 ; 11B30 ; 11B75

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