Sums, products, and ratios along the edges of a graph
Alon, Noga (Tel Aviv University. Schools of Mathematics and Computer Science)
Ruzsa, Imre (Hungarian Academy of Sciences. Alfréd Rényi Institute of Mathematics)
Solymosi, József (University of British Columbia. Department of Mathematics)

Data:	2020
Resum:	In their seminal paper Erdös 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 Erdös-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.
Nota:	The first named author is supported in part by NSF grant DMS-1855464, ISF grant 281/17, and the Simons Foundation. The second named author is supported in part by an OTKA NK 104183 grant. The third named author is supported in part by a NSERC and an OTKA NK 104183 grant.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Sumset ; Sum-product problems ; Incidence geometry
Publicat a:	Publicacions matemàtiques, Vol. 64 Núm. 1 (2020) , p. 143-155, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/362891
DOI: 10.5565/PUBLMAT6412006

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