Comptes Rendus
no. 8
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 Fox1 ; Yuval Wigderson1 ; Yufei Zhao2 
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.

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.

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Révisé le :
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DOI : 10.5802/crmath.101
Classification : 05D10, 11B30
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 
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     title = {A short proof of the canonical polynomial van der {Waerden} theorem},
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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/

[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

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