Erdős sumset conjecture

In additive combinatorics, the Erdős sumset conjecture is a conjecture which states that if a subset $A$ of the natural numbers $\mathbb {N}$ has a positive upper density then there are two infinite subsets $B$ and $C$ of $\mathbb {N}$ such that $A$ contains the sumset $B+C$ .^[1]^[2] It was posed by Paul Erdős, and was proven in 2019 in a paper by Joel Moreira, Florian Richter and Donald Robertson.^[3]

Notes

^ Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl (2015), "On a sumset conjecture of Erdős" (PDF), Canadian Journal of Mathematics, 67 (4): 795–809, arXiv:1307.0767, doi:10.4153/CJM-2014-016-0, S2CID 15626732
^ "Erdős Sumset conjecture". 20 August 2017.
^ Moreira, Joel; Richter, Florian (March 2019). "A proof of a sumset conjecture". Annals of Mathematics. 189 (2): 605–652. arXiv:1803.00498. doi:10.4007/annals.2019.189.2.4. JSTOR 10.4007/annals.2019.189.2.4. S2CID 119158401. Retrieved 16 July 2020.

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[1] Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl (2015), "On a sumset conjecture of Erdős" (PDF), Canadian Journal of Mathematics, 67 (4): 795–809, arXiv:1307.0767, doi:10.4153/CJM-2014-016-0, S2CID 15626732

[2] "Erdős Sumset conjecture". 20 August 2017.

[jfd1-3] Moreira, Joel; Richter, Florian (March 2019). "A proof of a sumset conjecture". Annals of Mathematics. 189 (2): 605–652. arXiv:1803.00498. doi:10.4007/annals.2019.189.2.4. JSTOR 10.4007/annals.2019.189.2.4. S2CID 119158401. Retrieved 16 July 2020.

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