Geodesic
A Construction for Partitions Which Avoid Long Arithmetic Progressions
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 409-414

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

For k ≥2, t ≥2, let W(k, t) denote the least integer m such that in every partition of m consecutive integers into k sets, atleast one set contains an arithmetic progression of t+1 terms. This paper presents a construction which improves the best previously known lower bounds on W(k, t) for small k and large t. 
Berlekamp, E.R. A Construction for Partitions Which Avoid Long Arithmetic Progressions. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 409-414. doi: 10.4153/CMB-1968-047-7
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Erdös, P. and Radó, R., Combinatorial theorems on classifications of subsets of a given set. Proceedings of the London Mathematical Society (3) 2(1952)417-439. Google Scholar

Folkman, J., private communication (1967). Google Scholar

Moser, L., On a theorem of van der Waerden. Canadian Mathematical Bulletin, 3 (1960) 23-25. Google Scholar

Schmidt, W.M., Two combinatorial theorems on arithmetic progressions. Duke Math. J. 29(1962)129-140. Google Scholar

van der Waerden, B.L., Beweis einer Baudet'schen Vermutung. Niew Archief voor Wiskunde, 15 (1925) 212-216. Google Scholar

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