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Density versions of Schur’s theorem for ideals generated by submeasures. (English) Zbl 1230.05036
Summary: We characterize ideals of subsets of natural numbers for which some versions of Schur’s theorem hold. These are similar to generalizations shown by {\it V. Bergelson} in [J. Comb. Theory, Ser. A 43, 338--343 (1986; Zbl 0607.10040)] and {\it P. Frankl}, {\it R. I. Graham} and {\it V. Rödl} in [J. Comb. Theory, Ser. A 54, No. 1, 95--111 (1990; Zbl 0738.05008)]. Additionally, we prove a generalization of an iterated version of Ramsey’s theorem.

MSC:
05A17Partitions of integers (combinatorics)
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References:
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