Hegarty, Peter Extremal subsets of \(\{1,\dots ,n\}\) avoiding solutions to linear equations in three variables. (English) Zbl 1157.05335 Electron. J. Comb. 14, No. 1, Research Paper R74, 22 p. (2007). 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 \(a+b \neq c\). Cited in 3 Documents MSC: 05D05 Extremal set theory 11P99 Additive number theory; partitions 11B75 Other combinatorial number theory PDFBibTeX XMLCite \textit{P. Hegarty}, Electron. J. Comb. 14, No. 1, Research Paper R74, 22 p. (2007; Zbl 1157.05335) Full Text: arXiv EuDML EMIS