Sums, products, and ratios along the edges of a graph

Noga Alon; Imre Ruzsa; József Solymosi

doi:10.5565/PUBLMAT6412006

Sums, products, and ratios along the edges of a graph

Noga Alon, Imre Ruzsa, József Solymosi

School of Computer Science

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In their seminal paper Erdos and Szemerédi formulated conjectures on the size of sumset and product set of integers. The strongest form of their conjecture is about sums and products along the edges of a graph. In this paper we show that this strong form of the Erdos–Szemerédi conjecture does not hold. We give upper and lower bounds on the cardinalities of sumsets, product sets, and ratio sets along the edges of graphs.

Original language	English
Pages (from-to)	143-155
Number of pages	13
Journal	Publicacions Matematiques
Volume	64
Issue number	1
DOIs	https://doi.org/10.5565/PUBLMAT6412006
State	Published - 2020

Funding

Funders	Funder number
Natural Sciences and Engineering Research Council of Canada
Simons Foundation
Hungarian Scientific Research Fund	NK 104183
UK Research and Innovation	104183
National Science Foundation	DMS-1855464
Israel Science Foundation	281/17

Keywords

Incidence geometry
Sum-product problems
Sumset

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10.5565/PUBLMAT6412006

Cite this

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Sums, products, and ratios along the edges of a graph

Abstract

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Keywords

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