A short proof of the canonical polynomial van der Waerden theorem

Jacob Fox; Yuval Wigderson; Yufei Zhao

doi:10.5802/crmath.101

Théorie des nombres

A short proof of the canonical polynomial van der Waerden theorem
[Une démonstration courte du théorème de van der Waerden polynomial canonique]

Jacob Fox ¹ ; Yuval Wigderson ¹ ; Yufei Zhao ²

¹ Department of Mathematics, Stanford University, Stanford, CA, USA
² Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 957-959.

Résumé
Abstract

Nous présentons une nouvelle démonstration courte du théorème de van der Waerden polynomial canonique, récemment établi par Girão.

We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girão.

Reçu le : 2020-07-09
Révisé le : 2020-07-21
Accepté le : 2020-07-26
Publié le : 2020-12-03

DOI : 10.5802/crmath.101

Classification : 05D10, 11B30

Affiliations des auteurs :

Jacob Fox ¹ ; Yuval Wigderson ¹ ; Yufei Zhao ²

¹ Department of Mathematics, Stanford University, Stanford, CA, USA
² Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2020__358_8_957_0,
     author = {Jacob Fox and Yuval Wigderson and Yufei Zhao},
     title = {A short proof of the canonical polynomial van der {Waerden} theorem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {957--959},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {8},
     year = {2020},
     doi = {10.5802/crmath.101},
     language = {en},
}

TY  - JOUR
AU  - Jacob Fox
AU  - Yuval Wigderson
AU  - Yufei Zhao
TI  - A short proof of the canonical polynomial van der Waerden theorem
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 957
EP  - 959
VL  - 358
IS  - 8
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.101
LA  - en
ID  - CRMATH_2020__358_8_957_0
ER  -

%0 Journal Article
%A Jacob Fox
%A Yuval Wigderson
%A Yufei Zhao
%T A short proof of the canonical polynomial van der Waerden theorem
%J Comptes Rendus. Mathématique
%D 2020
%P 957-959
%V 358
%N 8
%I Académie des sciences, Paris
%R 10.5802/crmath.101
%G en
%F CRMATH_2020__358_8_957_0

Jacob Fox; Yuval Wigderson; Yufei Zhao. A short proof of the canonical polynomial van der Waerden theorem. Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 957-959. doi : 10.5802/crmath.101. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.101/

Bibliographie
Cité par

[1] Vitaly Bergelson; Alexander Leibman Polynomial extensions of van der Waerden’s and Szemerédi’s theorems, J. Am. Math. Soc., Volume 9 (1996) no. 3, pp. 725-753 | DOI | MR | Zbl

[2] Pál Erdős; Ronald L. Graham Old and new problems and results in combinatorial number theory, Monographies de l’Enseignement Mathématique, 28, L’Enseignement Mathématique, 1980, 128 pages | MR | Zbl

[3] Pál Erdős; Richard Rado A combinatorial theorem, J. Lond. Math. Soc., Volume 25 (1950), pp. 249-255 | DOI | MR | Zbl

[4] António Girão A canonical polynomial van der Waerden’s theorem (https://arxiv.org/abs/2004.07766) | Zbl

[5] Loo Keng Hua Introduction to number theory, Springer, 1982 | MR | Zbl

[6] Yuriĭ V. Linnik An elementary solution of the problem of Waring by Schnirelman’s method, Mat. Sb., N. Ser., Volume 12(54) (1943), pp. 225-230 | MR | Zbl

[7] Endre Szemerédi On sets of integers containing no $k$ elements in arithmetic progression, Acta Arith., Volume 27 (1975), pp. 199-245 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique