Long arithmetic progressions in sumsets: Thresholds and Bounds

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dc.creatorSzemeredi, E.
dc.creatorVu, V.
dc.date2005-07-26
dc.date2005-08-11
dc.date.accessioned2026-07-07T05:22:00Z
dc.date.available2026-07-07T05:22:00Z
dc.descriptionFor a set $A$ of integers, the sumset $lA =A+...+A$ consists of those numbers which can be represented as a sum of $l$ elements of $A$ $$lA =\{a_1+... a_l| a_i \in A_i \}. $$ A closely related and equally interesting notion is that of $l^{\ast}A$, which is the collection of numbers which can be represented as a sum of $l$ different elements of $A$ $$l^{\ast} A =\{a_1+... a_l| a_i \in A_i, a_i \neq a_j \}. $$ The goal of this paper is to investigate the structure of $lA$ and $l^{\ast}A$, where $A$ is a subset of $\{1,2, ..., n\}$. As applications, we solve two conjectures by Erdös and Folkman, posed in sixties.
dc.identifierhttps://arxiv.org/abs/math/0507539
dc.identifierhttp://arxiv.org/abs/math/0507539
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75901
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11B25, 11P70, 11B75
dc.titleLong arithmetic progressions in sumsets: Thresholds and Bounds
dc.typetext

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