Séminaire CAESAR
de combinatoire additive
Séance du 16 février 2012
(14 heures, Jussieu, couloir 1525, salle 101):
Christian ELSHOLTZ
(TU Graz, Autriche)
A survey on additive and multiplicative decompositions of
sumsets and of shifted sets
The set of "Sums of two squares" has an additive and a multiplicative
description.
We give a survey on results on sumsets A+B being equal to
(or being a subset of)
a multiplicatively defined set, for example the set of primes.
Conversely, we study shifted copies of a multiplicatively
defined set (such as the shifted primes),
and ask if these sets can be multiplicatively decomposed.
The methods involved include the large sieve and extremal graph theory.
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