Full Dimensional Sets Without Given Patterns

By P. Maga. 2011

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Finite chains inside thin subsets of ℝd (2014, background): “It is reasonable to wonder whether the assumptions of Theorem 1.1 can be weakened, but the following result due to Maga ([10]) shows that conclusion may fail even if we replace the upper Lebesgue density condition with the assumption that the set is of dimension d. Theorem 1.2.”
Finite configurations in sparse sets (2013, background): “Harangi, Keleti, Kiss, Maga, Máthé, Matilla, and Strenner [15] give upper bounds on C(n, θ) (which they show is tight for θ = 0, π), and Máthé [28] provides lower bounds.”