A short proof of the canonical polynomial van der Waerden theorem

Jacob Fox; Yuval Wigderson; Yufei Zhao

doi:10.5802/crmath.101

Number Theory

A short proof of the canonical polynomial van der Waerden theorem

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.

Abstract
Résumé

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

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

Received: 2020-07-09
Revised: 2020-07-21
Accepted: 2020-07-26
Published online: 2020-12-03

DOI: 10.5802/crmath.101

Classification: 05D10, 11B30

Author's affiliations:

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@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/

References
Cited by

[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

Cited by Sources:

Comments - Policy