Erdős sumset conjecture
From HandWiki
Short description: Conjecture in additive combinations about subsets of natural numbers
In additive combinatorics, the Erdős sumset conjecture is a conjecture which states that if a subset [math]\displaystyle{ A }[/math] of the natural numbers [math]\displaystyle{ \mathbb{N} }[/math] has a positive upper density then there are two infinite subsets [math]\displaystyle{ B }[/math] and [math]\displaystyle{ C }[/math] of [math]\displaystyle{ \mathbb{N} }[/math] such that [math]\displaystyle{ A }[/math] contains the sumset [math]\displaystyle{ B+C }[/math].[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]
See also
Notes
- ↑ Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl (2015), "On a sumset conjecture of Erdős", Canadian Journal of Mathematics 67 (4): 795–809, doi:10.4153/CJM-2014-016-0, https://www.math.uci.edu/~isaac/B+Cfinal.pdf
- ↑ "Erdős Sumset conjecture". 20 August 2017. https://joelmoreira.wordpress.com/2017/08/20/659/.
- ↑ Moreira, Joel; Richter, Florian (March 2019). "A proof of a sumset conjecture". Annals of Mathematics 189 (2): 605–652. doi:10.4007/annals.2019.189.2.4. https://www.jstor.org/stable/10.4007/annals.2019.189.2.4. Retrieved 16 July 2020.
 |  |
