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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  and
Hamza Si Kaddour
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.

Keywords

05A99Ramsey Theoryinfinite sums(m, p, c)-sets
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 96 - 102
Copyright
Copyright © Canadian Mathematical Society 1993

References

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