Geodesic
Monochromatic sums and products in $\mathbb N$
Joel Moreira1
1 Northwestern University, Evanston, IL
Annals of mathematics, Tome 185 (2017) no. 3, pp. 1069-1090.

Voir la notice de l'article provenant de la source Annals of Mathematics website

An old question in Ramsey theory asks whether any finite coloring of the natural numbers admits a monochromatic pair $\{x+y,xy\}$. We answer this question affirmatively in a strong sense by exhibiting a large new class of nonlinear patterns that can be found in a single cell of any finite partition of $\mathbb N$. Our proof involves a correspondence principle that transfers the problem into the language of topological dynamics. As a corollary of our main theorem we obtain partition regularity for new types of equations, such as $x^2-y^2=z$ and $x^2+2y^2-3z^2=w$.
DOI : 10.4007/annals.2017.185.3.10

Joel Moreira 1

1 Northwestern University, Evanston, IL 
@article{10_4007_annals_2017_185_3_10,
     author = {Joel Moreira},
     title = {Monochromatic sums and products in $\mathbb N$},
     journal = {Annals of mathematics},
     pages = {1069--1090},
     publisher = {mathdoc},
     volume = {185},
     number = {3},
     year = {2017},
     doi = {10.4007/annals.2017.185.3.10},
     mrnumber = {3664819},
     zbl = {06731866},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.3.10/}
}
TY  - JOUR
AU  - Joel Moreira
TI  - Monochromatic sums and products in $\mathbb N$
JO  - Annals of mathematics
PY  - 2017
SP  - 1069
EP  - 1090
VL  - 185
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.3.10/
DO  - 10.4007/annals.2017.185.3.10
LA  - en
ID  - 10_4007_annals_2017_185_3_10
ER  - 
%0 Journal Article
%A Joel Moreira
%T Monochromatic sums and products in $\mathbb N$
%J Annals of mathematics
%D 2017
%P 1069-1090
%V 185
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.3.10/
%R 10.4007/annals.2017.185.3.10
%G en
%F 10_4007_annals_2017_185_3_10
Joel Moreira. Monochromatic sums and products in $\mathbb N$. Annals of mathematics, Tome 185 (2017) no. 3, pp. 1069-1090. doi : 10.4007/annals.2017.185.3.10. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.3.10/

Cité par Sources :