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Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 439-441 (mai 2012)
Doi : 10.1016/j.crma.2012.04.011
Received : 26 Mars 2012 ;  accepted : 4 April 2012
Partition regularity and the primes
Régularité de partitions et les nombres premiers
 

Thái Hoàng Lê
Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200 Austin, TX 78712, USA 

Abstract

The purpose of this Note is to point out, as a simple yet nice consequence of Green and Taoʼs program on counting linear patterns in the primes and Deuberʼs work on partition regularity, that if a system of equations is partition regular over the positive integers, then it is also partition regular over the sets   as well as  . This answers a question of Li and Pan.

The full text of this article is available in PDF format.
Résumé

Dans cette Note, on montre, comme une conséquence simple du programme de Green et Tao sur le comptage de configurations linéaires dans les nombres premiers et du travail de Deuber sur la régularité de partitions, que si un système dʼéquations est régulier par rapport aux partitions des nombres entiers, alors il est régulier par rapport aux partitions des ensembles   ainsi que  . Cela répond à une question de Li et de Pan.

The full text of this article is available in PDF format.


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