A Note on sparse supersaturation and extremal results for linear homogeneous systems
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We study the thresholds for the property of containing a solution to a linear homogeneous system in random sets. We expand a previous sparse Sz\'emeredi-type result of Schacht to the broadest class of matrices possible. We also provide a shorter proof of a sparse Rado result of Friedgut, R\
CitationSpiegel, C. A Note on sparse supersaturation and extremal results for linear homogeneous systems. "Electronic journal of combinatorics", 25 Agost 2017, vol. 24, núm. 3, p. 1-14.