Geodesic
A Lattice Point Problem Related to Sets Containing No l-Term Arithmetic Progression
Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 535-538

Voir la notice de l'article provenant de la source Cambridge University Press

In 1927 van der Waerden [6] proved that given positive integers k and l, there exists an integer W such that if 1, 2, ..., W are partitioned into k or fewer classes, then at least one class contains an l-term arithmetic progression (l-progression). Let W(k, l), be the smallest such integer W. It would be of interest to find a reasonable upper estimate for W(k, l), say one that could be written down. 
Riddell, J. A Lattice Point Problem Related to Sets Containing No l-Term Arithmetic Progression. Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 535-538. doi: 10.4153/CMB-1971-095-0
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[1] 1. Hales, A. W. and Jewett, R. I., Regularity and positional games, Trans. Amer. Math. Soc. 106 (1963), 222-229. Google Scholar

[2] 2. Rankin, R. A., Sets of integers containing not more than a given number of terms in arithmetical progression, Proc. Roy. Soc. Edinburgh Sect. A., 65 (1962), 332-344. Google Scholar

[3] 3. Robbins, H., A remark on Stirling's formula, Amer. Math. Monthly 62 (1955), 26-29. Google Scholar

[4] 4. Roth, K. F., On certain sets of integers, J. London Math. Soc. 28 (1953), 104-109. Google Scholar

[5] 5. Szemerédi, E., On sets of integers containing no four elements in arithmetic progression, Acta Math. Acad. Sci. Hung. 20 (1969), 89-104. Google Scholar

[6] 6. van der Waerden, B. L., Beweis einer Baude'schen Vermutung, Nieuw Arch. Wisk. Ser. 2 15 (1927), 212-216. Google Scholar

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