Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T17:52:47.576Z Has data issue: false hasContentIssue false

Some Progression-Free Partitions Constructed using Folkman's Method

Published online by Cambridge University Press:  20 November 2018

John R. Rabung*
Affiliation:
Department Of Mathematical Sciences Virginia Commonwealth University901 West Franklin Street Richmond, Virginia23284
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Almost from the day that B. L. van der Waerden [10] proved his now famous theorem on arithmetic progressions, mathematicians have been working to find a new or an improved constructive proof of that result, but without much success.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Berlekamp, E. R., A construction for partitions which avoid long arithmetic progressions, Canad. Math. Bull. 11 (1968), 409-414.Google Scholar
2. V. Chvátal, Some unknown van der Waerden numbers, Combinatorial Structures and Their Applications, Guy, R. K. et al. (editors) Gordon and Breach, 1970, 31-33.Google Scholar
3. P. Erdös, Some recent advances and current problems in number theory, Lectures on Modern Mathematics, Vol. 3, Saaty, T. L. (editor), Wiley, New York, 1965, 196-244.Google Scholar
4. Erdös, P. and Lovász, L., Problems and results on 3-chromatic hypergraphs and some related questions, Infinite and finite sets, Colloqu. Math. Soc. Janos Bolyai lo, Hajnol, Rado, and Sos (eds), North Holland, Amsterdam, 1975, 609-627 Google Scholar
5. P. Erdös and Rado, R., Combinatorial theorems on classifications of subsets of a given set, Proc. London Math. Soc, 2 (1952), 417-439.Google Scholar
6. Moser, L., On a theorem of van der Waerden, Canad. Math. Bull. 3 (1960), 23-25.Google Scholar
7. Rabung, J. R., On applications of van der Waerden's theorem, Math. Mag. 48 (1975), 142-148.Google Scholar
8. Schmidt, W. M., Two combinatorial theorems on arithemtic progressions, Duke Math. J. 29 (1962), 129-140.Google Scholar
9. Spencer, Joel, Ramsey's Theorem — a new lower bound, J. Combinatorial Theory 18 (1975), 108-115.Google Scholar
10. van der Waerden, B. L., Beweis einer Baudet'schen Vermutung, Nieuw Arch. Wisk., 15 (1927) 212-216.Google Scholar
11. Vegh, E., Hauptman, H., and Fisher, J., Tables of all Primitive Roots for Primes Less than 5000, Mathematics Research Center Report 70-5, Naval Research Laboratory, Washington, D.C. 1970.Google Scholar
12. Western, A. E. and Miller, J. C. P., Tables of Indices and Primitive Roots, Royal Society Mathematical Tables, Vol. 9, 1968, (University Press Cambridge).Google Scholar