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SUMMARY:Marcelo Sales\, On Pisier type problems
DESCRIPTION:A subset $A\subseteq \mathbb Z$ of integers is free if for every two distinct subsets $B\, B’\subseteq A$ we have \[ \sum_{b\in B}b\neq \sum_{b’\in B’} b’.\]Pisier asked if for every subset $A\subseteq \mathbb Z$ of integers the following two statement are equivalent: \n(i) $A$ is a union of finitely many free sets.\n(ii) There exists $\epsilon>0$ such that every finite subset $B\subseteq A$ contains a free subset $C\subseteq B$ with $|C|\geq \epsilon |B|$. \nIn a more general framework\, the Pisier question can be seen as the problem of determining if statements (i) and (ii) are equivalent for subsets of a given structure with prescribed property. We study the problem for several structures including $B_h$-sets\, arithmetic progressions\, independent sets in hypergraphs and configurations in the euclidean space. This is joint work with Jaroslav Nešetřil and Vojtech Rödl.
URL:https://dimag.ibs.re.kr/event/2023-03-09/
LOCATION:Zoom ID: 224 221 2686 (ibsecopro)
CATEGORIES:Virtual Discrete Math Colloquium
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