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Extremal subsets of \(\{1,\dots ,n\}\) avoiding solutions to linear equations in three variables. (English) Zbl 1157.05335

Summary: We refine previous results to provide examples, and in some cases precise classifications, of extremal subsets of \(\{1,\dots,n\}\) containing no solutions to a wide class of non-invariant, homogeneous linear equations in three variables, i.e.: equations of the form \(ax+by=cz\) with \(a+b \neq c\).

MSC:

05D05 Extremal set theory
11P99 Additive number theory; partitions
11B75 Other combinatorial number theory
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