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

Noga Alon, Imre Ruzsa, József Solymosi

Research output: Contribution to journalArticlepeer-review

2 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 languageEnglish (US)
Pages (from-to)143-155
Number of pages13
JournalPublicacions Matematiques
Volume64
Issue number1
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Incidence geometry
  • Sum-product problems
  • Sumset

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