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On a Maximality Property of Partition Regular Systems of Equations

Published online by Cambridge University Press:  20 November 2018

Hanno Lefmann
Affiliation:
Fakultät für Mathematik SFB 343 Universität Bielefeld Postfach 8640 W-4800 Bielefeld 1 Germany
Hamza Si Kaddour
Affiliation:
Départment de Mathématiques Université Claude Bernard Lyon 1 - 43 Bd - du 11 Novembre 1918, 69622 Villeurbanne France
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Abstract

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In this note we will study the following problem. For a given partition regular system of equations, which equations can be added to this system without introducing new variables, such that the new augmented system is again partition regular. It turns that the Hindman system on finite sums as well as the Deuber-Hindman system on finite sums of (m, p, c)-sets are maximal in this sense.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

References

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[GRS 80] Graham, R. L., Rothschild, B. L. and Spencer, J. H., Ramsey theory, John Wiley, New York, 1980.Google Scholar
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[vdW 27] van, B. L. der Waerden, Beweis einer Baudetschen Vermutung, Nieuw Arch. Wisk. 15(1927), 212— 216.Google Scholar
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